Modulo Challenge (Addition and Subtraction) Modular multiplication. Practice: Modular multiplication. Modular exponentiation. This is the currently selected item. Fast modular exponentiation. Fast Modular Exponentiation. Modular inverses. The Euclidean Algorithm. Next lesson. Primality test How to calculate a raised to power b modulo n? It consists in an exponentiation followed by a modulus, but it exists optimized algorithms with big numbers to return a fast result without having to actually perform the calculation (called fast, thanks to mathematical simplifications) This is a really useful function that I thought needed to be explained.When dealing with security methods, like RSA or the Diffie-Hellman, or finding primes. Modular Exponentiation Calculator Free and fast online Modular Exponentiation (ModPow) calculator. Just type in the base number, exponent and modulo, and click Calculate. This Modular Exponentiation calculator can handle big numbers, with any number of digits, as long as they are positive integers

Homework Statement In my Number Theory class, we learned how to calculate the value of large exponents modulo primes using Euler's Theorem. I understand how to do this with exponents larger than the value of the totient function of the prime, which is p-1, but what about when the exponent is.. The big gain in power arises from employing lcm vs. product to combine exponents: aj ≡ 1 (mod m) ak ≡ 1 (mod n) } ⇒ alcm (j, k) ≡ 1 (modlcm(m, n)) For example, if n is coprime to 2, 3, 5 then Euler's theorem implies that n64 ≡ 1 (mod240), versus Carmichael's theorem, which yields the much stronger result that n4 ≡ 1 (mod240) Calculating Large Exponents Background: This is a quick article as to how to calculate the exponents of large numbers quickly and efficiently. Starting with a basic multiplication algorithm, it gives subsequently faster algorithms and a few quick examples

The problem with above solutions is, overflow may occur for large value of n or x. Therefore, power is generally evaluated under modulo of a large number. Below is the fundamental modular property that is used for efficiently computing power under modular arithmetic When making computations modulo a large number, one does not first make the whole computation in N and then take the remainder of the result, because for something like an exponentiation the intermediate result would be exceedingly large. Rather, the result is calculated with reductions modulo n at each step This video shows viewers how to calculate x to the power of y quickly by dramatically reducing the number of operations required to calculate the value of th..

Modular Multiplication Using Intermediate Modulo-n ReductionsWhen multiplying numbers using modular arithmetic, we can exploiting some basic properties to keep the range of intermediate results that we have to work to a range that is strictly less than n 2.This means that we can evaluate the above expression, 9 11 mod 13, and never work with any number as large as 169, which is clearly a. ** Modular Exponentiation Calculator**,Successive Squaring Calculato increasing the exponent n by 4 will never change the remainder when dividing by 13, and 5 n⌘ 5 +4 (mod 13) for all exponents n. Determining the remainder of 5n when dividing by 13 then requires us to determine whether the exponent n is divisible by 4. If it is divisible by 4, then the remainder must be 1. Otherwise

How can I solve large exponents without a calculator, e.g. (0.95) ^10? I doubt if there is a general efficient method apart from using logs and exponentials. But calculating these manually needs a lot of knowledge*. Whatever method you use you wil.. The operation of modular exponentiation calculates the remainder when an integer b (the base) raised to the e th power (the exponent), be, is divided by a positive integer m (the modulus). In symbols, given base b, exponent e, and modulus m, the modular exponentiation c is: c = be mod m. From the definition of c, it follows that 0 ≤ c < m Calculator Use. This calculator performs exponentiation, xn, for positive integer bases, x, with positive integer exponents, n. It allows large numbers; up to 7 digits for x and up to 5 digits for n. If you need larger numbers, please contact me with a request. If you want to operate on smaller values that include decimals and negative numbers. PowerMod Calculator Computes (base) (exponent) mod (modulus) in log(exponent) time

The output: BigInteger Mod Power . BigInteger modPow(BigInteger exponent, BigInteger m) returns a BigInteger whose value is (this exponent mod m) In competitions, for calculating large powers of a number we are given a modulus value(a large prime number) because as the values of is being calculated it can get very large so instead we have to calculate (%modulus value.) We can use the modulus in our naive way by using modulus on all the intermediate steps and take modulus at the end Enter an integer number to calculate its remainder of Euclidean division by a given modulus. 15 4 375. Just type in the base number exponent and modulo and click Calculate. The most efficient method consists of. Function powmod base b exponent e modulus m if m 1 then return 0 This is also called as the modulus. Use this mod / modulo. Calculating Large Exponents Background: This is a quick article as to how to calculate the exponents of large numbers quickly and efficiently. Starting with a basic multiplication algorithm, it gives subsequently faster algorithms and a few quick examples Mod calculator with exponents. Modular Exponentiation Calculator - Power Mod, PowerMod Calculator Computes (base)(exponent) mod (modulus) in log( exponent) time. Base: Exponent: Modulus: be MOD m = It consists in an exponentiation followed by a modulus, but it exists optimized algorithms with big numbers to return a fast result without having to actually perform the calculation (called fast.

Then it raises x M to the power q, multiplies this value with x N, and then assigns x N the result of this computation and n M the value n M modulo n N. Further applications. The same idea allows fast computation of large exponents modulo a number. Especially in cryptography, it is useful to compute powers in a ring of integers modulo q How to Solve Large Exponents, This video shows viewers how to calculate x to the power of y quickly by dramatically reducing Duration: 4:37 Posted: Aug 15, 2009 Modulo power for large numbers represented as strings Last Updated: 30-01-2019 Given two numbers sa and sb represented as strings, find a b % MOD where MOD is 1e9 + 7. The numbers a and.

T h e idea of binary exponentiation is, that we can reduce the power by dividing it by 2, let's take an example we have to calculate 2¹⁰, so we can write 2¹⁰ as (2²)⁵, or (2*2)⁵. 2*2 can be calculated in constant time and initially, we have to multiply 2with itself for 9 times to get the value of 2¹⁰, but here we can get the. On the other hand, if A is large then we do need techniques to simplify 'A mod B', because we don't have such a 7^4 modulo 13 == 9. 7^256 modulo 13 == 9. 7^4^4^2 is not the better way because the number is larger than 7^10 and the given calculator's memory cannot hold numbers larger than that E.g., Mersenne Prime number: 618970019642690137449562111 used as default exponent value has 89 bits (see Bit length). To safely handle such exponents, we must use fast exponentiation algorithms. In the Polynomial power expansion calculator, we already used fast exponentiation algorithm based on a power tree. It allows minimizing the number of. Similar calculators. • Modular exponentiation. • Modular arithmetic. • Factorial. • Modular Multiplicative Inverse. • Mod calculator. • Math section ( 247 calculators ) local_offer big integer exponentiation integer Math modular modulus power. PLANETCALC, Modular exponentiation

- How modulo calculator works for big input numbers ? Given two input numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder from the division of a by n. Example : 14 Mod 3. Math problem 14 mod 3 would evaluate to 2 because 14 divided by 3 leaves a remainder of 2
- This will calculate: Base Exponent mod Mod Base = Exponent
- Modulo is also referred to as 'mod.' The standard format for mod is: a mod n Where a is the value that is divided by n. For example, you're calculating 15 mod 4. When you divide 15 by 4, there's a remainder. 15 / 4 = 3.75. Instead of its decimal form (0.75), when you use the mod function in a calculator, the remainder is a whole number
- For a private key operation, the exponentiations used big exponents, and the savings implied by Montgomery multiplications dwarf these overheads, but this might not be true for a short exponent. Therefore, even if your accelerator did support a 4096-bit modulus, it is unclear whether this would have really provided some speedup for your public.
- This modulo calculator is a handy tool if you need to find the result of modulo operations. All you have to do is input the initial number x and integer y to find the modulo number r, according to x mod y = r.Read on to discover what modulo operations are, how to calculate modulo and how to use this calculator correctly
- Sometimes, you are asked to calculate the combination or permutation modulo a number, for example $$$^nC_k \mod p$$$. Here I want to write about a complete method to solve such problems with a good time complexity because it took me a lot of googling and asking to finally have the complete approach

This is a C++ program to implement Modular Exponentiation Algorithm.AlgorithmBegin function modular(): // Arguments: base, exp, mod. // Body of t. Big Number Calculator. The calculator below can compute very large numbers. Acceptable formats include: integers, decimal, or the E-notation form of scientific notation, i.e. 23E18, 3.5e19, etc. X! Most scientific and graphing calculators can only display possibly up to 10 decimal places of accuracy. While this is enough in most instances of. Exponent Definition. The Exponent Calculator is an easy way to enter in any number and any exponent and then find the solution. Simply enter in any number and then any number as an exponent and press the calculate button! The simple definition of an exponent is that an exponent (the small raised number to the right of another number) represents. Units digit of Large Numbers - number raised to power. One of the ways of finding the units digit of a power is by finding the remainder when that number is divided by 10. Identify the units digit in the base 'x' and call it say 'l'. {For example, If x = 24, then the units digit in 24 is 4. Hence l = 4.

To calculate modulo using inverse modulo calculator, follow the below steps: This equation can help in the handling of large numbers, and we do not immediately know modulo of the great numbers. You can use our exponent calculator to calculate the exponent for above example. Moreover,. Let's say you wanted to calculate the large power of a number modulo another such as 7^39 mod 1000. The most naive way to do this would be to multiply 7 by itself 39 times and then take the remainder when divided by 1000, aka the last 3 digits. However, this technique quickly becomes unmanageable, especially since 7^39 has 32 digits, which would lead to a lot of work and the opportunity to.

- how_to_do_large_exponents_without_a_calculator 2/16 How To Do Large Exponents Without A Calculator [Books] How To Do Large Exponents Without A Calculator Algebra and Trigonometry-Jay P. Abramson 2015-02-13 The text is suitable for a typical introductory algebra course, and was developed to be used flexibly
- Free Modulo calculator - find modulo of a division operation between two numbers step by step. This website uses cookies to ensure you get the best experience. Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics
- The numbers entered must be positive integers except for the base, that may be negative too, and the modulo, that must only be greater than zero. Base: Exponent
- We can use these conversions to calculate the modulus of not-too-huge numbers on a standard calculator. Modulus on a Standard Calculator. To calculate a mod n on a standard calculator. Divide a by n; Subtract the whole part of the resulting quantity; Multiply by n to obtain the modulu
- Addition modulo p-subtraction modulo p multiplication modulo p division modulo p available for all numbers if the modulus is a prime number only exponentiation modulo p. Thus X 3 7 11 4 6 5 11 4 6 5 7 6 3504. Just type in the number and modulo and click Calculate. For a more comprehensive mathematical tool see the Big Number Calculator
- Answer to: How to calculate modulo with exponents? By signing up, you'll get thousands of step-by-step solutions to your homework questions. You..

- al: $ python >>> pow(5, (13**(23**2011)), 24) The first number is the base, the second number is the exponent, the third number is an optional argument..
- All you need to do is compute the power incrementally, modulo 10 m. In this article, I will discuss three methods — all based on modular exponentiation and the laws of exponents — for finding the ending digits of a positive power of two. The techniques I use are easily adapted to powers of any number. 1. Ad Hoc Exponentiatio
- the ElGamal PKC, Alice needs a large prime number p for which the discrete logarithm problem in F⁄ p is di-cult, and she needs an element g modulo p of large (prime) order. She may choose p and g herself, or they may have been preselected by some trusted party such as an industry panel or government agency
- Just type in the base number, exponent and modulo, and click Calculate. This Modular Exponentiation calculator can handle big numbers, with any number of digits, as long as they are positive integers. For a more comprehensive mathematical tool. About Modulo Calculator . The Modulo Calculator is used to perform the modulo operation on numbers.
- To calculate the value of the modulo inverse, use the extended euclidean algorithm which find solutions to the Bezout identity $ au + bv = \text{G.C.D.}(a, b) $. Here, the gcd value is known, it is 1 : $ \text{G.C.D.}(a, b) = 1 $, thus, only the value of $ u $ is needed.. Example: $ 3^-1 \equiv 4 \mod 11 $ because $ 4 \times 3 = 12 $ and $ 12 \equiv 1 \mod 11
- I am able to
**calculate**the**modulo**of smaller no.s by a c program. But when i am trying to**calculate**larger no.s like 658 and 185 , i am getting wrong answers. Obvious explanation is that 658^185 is a very**large**no. and not in the range of the int datatype

- e the power, modulo, greatest common divisor (GCD), and least common multiple (LCM) of large integer numbers. To use the calculator, simply type in the correct numbers in decimal format and click on any button below
- How to Calculate Modulo: An Example. Let's say we want to calculate 100 mod 32. Perform the division: 100 / 32 = 3.125. Retain the integer (3), and multiply it by the divisor (32): 3 × 32 = 96. 100 − 96 is 4. As such, 100 mod 32 = 4. You may also be interested in our Significant Figures Calculator or/and Online Scientific Notation Calculator
- If you know the exponent beforehand, there is a slightly more efficient way to subdivide the exponentiation, especially if the exponent is large. For example, with this algorithm quoted above, n^15 evaluates into the following sequence of six multiplications: And if it does, it probably cannot calculate trigonometry at hardware level

- Just type in the base number, exponent and modulo, and click Calculate. This Modular Exponentiation calculator can handle big numbers, with any number of digits, as long as they are positive integers.. For a more comprehensive mathematical tool, see the Big Number Calculator The calculator finds polynomial factors modulo p using Elwyn Berlekamp.
- 32 can be written as 11 x 2 + 10 or 32 = 11 x 3 - 1. Accordingly, positive remainder of 32 is 10 and its Negative remainder is -1. Similarly, 64 can be written as 11 x 5 + 9 or 64 = 11 x 6 - 2. Which gives positive remainder of 64 to be 9 and its Negative remainder to be -2. Also, 96 can be written as 11 x 8 + 8 or 96 = 11 x 9 - 3
- The procedure to use the mod calculator is as follows: Step 1: Enter two numbers in the respective input field. Step 2: Now click the button Solve to get the modulo value. Step 3: Finally, the modulo of the given numbers will be displayed in the output field

* public BigInteger modPow(BigInteger exponent, BigInteger m) Parameters*. exponent − The exponent. m − The modulus. Return Value. This method returns a BigInteger object whose value is this exponent mod m. Exception. ArithmeticException − If m ≤ 0 or the exponent is negative and this BigInteger is not relatively prime to m. Exampl For example, g c d ( 4, 10) = 2. The interesting thing is that if two numbers have a gcd of 1, then the smaller of the two numbers has a multiplicative inverse in the modulo of the larger number. It is expressed in the following equation: x ∈ Z p, x − 1 ∈ Z p gcd ( x, p) = 1. The above just says that an inverse only exists if the greatest. You will find that for much smaller factorials that this is true. 15! also has the last 2 digits of 00, for example. You can guarantee that the smallest number n such that the last 2 digits of n! are 0 that all numbers larger than n also have this property

#Calculate exponents in the Python programming language. In mathematics, an exponent of a number says how many times that number is repeatedly multiplied with itself (Wikipedia, 2019). We usually express that operation as b n, where b is the base and n is the exponent or power. We often call that type of operation b raised to the n-th power, b raised to the power of n, or most. ** The value resulting from Context**.power(x, y, modulo) is equal to the value that would be obtained by computing (x**y) % modulo with unbounded precision, but is computed more efficiently. The exponent of the result is zero, regardless of the exponents of x, y and modulo. The result is always exact. quantize (x, y) Modulo calculator. Use our umbrella comparison tool to find out your potential take-home pay and benefits. Get an instant take-home pay result and compare different umbrella companies Umbrella broker for public & private sectors with fast turnaround & low processing fees.Use our take-home calculator or speak to our dedicated team of experts today Calculate Modulo Enter two numbers, with the.

An online exponent calculator helps you to solve the exponent operations and determine the value of any positive or negative integer raised to nth power. Also, this exponential calculator shows the results of the fractional or negative power of any number. Here we provide you all the related data of exponent, manual calculations, exponentiation. How to make calculator in python. So friends, you can see that whatever is the sensitivity of all that is left to right. But you will see that right to left of exponents. In this way, Python uses associativity rule and precedence rule. Hope you understand how to make calculator in Python

All you have to do is select the start and end date, and the calculator will determine the months, weeks, and days between the two. This site uses cookies from Google to deliver its services and to analyze traffic. Here's what those different modes do. - The app's icon has changed to match the new guidelines. Enter the second number 200 Press the = key. You can do simple or advanced. Straightforward method []. The most straightforward method of calculating a modular exponent is to calculate b e directly, then to take this number modulo m.Consider trying to compute c, given b = 4, e = 13, and m = 497:. One could use a calculator to compute 4 13; this comes out to 67,108,864.Taking this value modulo 497, the answer c is determined to be 445

In cryptography, the exponent and the modulo are large numbers with hundreds or even thousands of decimal digits. For example, it can be verified that where. The modulus in this example is small enough so that all the reduction modulo can be done by a hand-held calculator. For example, take the first squaring When an exponent calculation is too big for a calculator to handle we have to break the process into smaller pieces using the following exponent law. If 'is a big exponent, then write '= k+ jfor two smaller numbers kand j. We can simplify as a'(mod n) = ak(mod n) aj(mod n) Example 12 (Modular Arithmetic Exponent Law 2). Here is an exampl * In RSA encoding and decoding algorithm, we need to calculate modular exponents (with a large exponent)*. /* return a^e mod n precondition: exponent e >=1 n >1 */ int exp(int a, int e, int n) Implement this function recursively, using the following two laws on exponents to cut down the number of mulitplication operations

Modular Exponentiation Calculator Boxentri . formed by modular exponentiation of the number a to the power x modulo P (ax gorithms [14, 15, 16], the process of multiplying large numbers by the module is ac-celerated First off, some important identities about the modulo operator: ( a mod m) + ( b mod m) mod m = a + b mod m. ( a mod m) − ( b mod m) mod m = a − b mod m. ( a mod m) ⋅ ( b mod m) mod m = a ⋅ b mod m. These identities have the very important consequence in that you generally don't need to ever store the true values of the large numbers. This explanation is the best I have seen so far! 5 6 = 1 mod 7, you can see this either by computing 5 6 or by using Fermat's Little Theorem. It then follows that 5 6m = (5 6) m = 1 m = 1 mod 7 for any integer m. So if we write 7121 as 6m+k for some m & k, we have 5 7121 = 5 6m+k = 5 6m .5 k = 1.5 k = 5 k mod 7 is the divisor. is the quotient. is the remainder. Sometimes, we are only interested in what the remainder is when we divide by . For these cases there is an operator called the modulo operator (abbreviated as mod). Using the same , , , and as above, we would have: We would say this as modulo is equal to

The last digit repeats in a pattern that is 4 digits long, 7,9,3,1. If you complete the table for 358 rows how many times will this pattern repeat? 358 divided by 4 is 89 with a remainder of 2 so the pattern will repeat 89 times and then there are two more rows. These rows then have 7 and 9 in the second column so the last digit of 7 358 is 9 The method in the other answer is didactic, but requires backtracking earlier calculations, and thus having kept these or use of recursion, which is undesirable in constrained environments as often used for crypto.. Another commonly taught method is the full extended Euclidean algorithm, which finds Bézout coefficients without recursion.However that requires keeping track of 6 quantities. It's actually possible to do this on a simple four-function calculator. Certainly, 7 29 is too **large** for the calculator to handle by itself, so we need to break the problem down into more manageable chunks. First, break the **exponent** (29) into a sum of powers of two. That is, 29 = 16 + 8 + 4 + 1 = 2 4 + 2 3 + 2 2 + 2 Modular arithmetic is a system of arithmetic for integers, which considers the remainder. In modular arithmetic, numbers wrap around upon reaching a given fixed quantity (this given quantity is known as the modulus) to leave a remainder. Modular arithmetic is often tied to prime numbers, for instance, in Wilson's theorem, Lucas's theorem, and Hensel's lemma, and generally appears in fields.

Exponent is a Power of Two. If c ← b e (mod m) and. e = 2 k. We can compute c using the squares method - this allows for fast computation of large positive integer powers of a number. From rules of indices: (b e) f = b ef. For example, this allows a⁸, can be represented as ((a²)²)². If you calculate a⁸ naively The modulo operation (abbreviated mod, or % in many programming languages) is the remainder when dividing. For example, 5 mod 3 = 2 which means 2 is the remainder when you divide 5 by 3. Converting everyday terms to math, an even number is one where it's 0 mod 2 — that is, it has a remainder of 0 when divided by 2 Overview. Modular arithmetic is simply arithmetic that is restricted to a finite set of elements. For our purposes, that set of elements will be the set of all non-negative integers less than some integer n (greater than 1) where n is called the modulus of the set. This is just a fancy way of saying that our set consists off all the integers from zero up to (but not including) n n. Using the modulo formula, we calculate n! modulo p without calculating n!, by starting with x = 1, and then for i = 1, 2, 3,., n we replace x with (x * i) modulo p. We always have x < p and i < n, so we only need enough precision to calculate x * p, not the much higher precision to calculate n!. So to calculate n! modulo p for p ≥ 2 we.

Write a function to calculate modular exponents In RSA encoding and decoding algorithm, we need to calculate modular exponents (with a large exponent). /* return a^e mod n precondition: exponent e >= n > */ int exp(int a, int e, int n) Implement this function recursively, using the following two laws on exponents to Output. Enter a base number: 2.3 Enter an exponent: 4.5 2.3^4.5 = 42.44. The programs above can only calculate the power of the base number if the exponent is positive. For negative exponents, use the following mathematical logic: base (-exponent) = 1 / (base exponent ) For example, 2 -3 = 1 / (2 3 This calculator can handle large numbers, with any number of digits, as long as they are integers. Calculator. Numeral System. Arithmetic. Number (a) Copy Paste. Number (b) Copy Paste. Calculate. a + b a - b a * b a / b a b a MOD b a -1 MOD b a AND b a OR b a XOR b. Result. Big integer numbers are numbers that are much larger than our usual. Free and fast online Modular Exponentiation (ModPow) calculator. Just type in the base number, exponent and modulo, and click Calculate. This Modular Exponentiation calculator can handle big numbers, with any number of digits, as long as they are positive integers.. For a more comprehensive mathematical tool, see the Big Number Calculato exponent modulo c++; how to find exponent value in cpp; exponent operator cpp; how to do exponentiation in c++; exponent operatoer in c++; exponents cpp; how to use exponent in c++; calculate exponent in c++; c++ how to use exponent; exponent cpp; how to write exponent in c++; c++ exponent without using pow; use exponent in c++; calculating.

Basic Math. Math Calculator. Step 1: Enter the expression you want to evaluate. The Math Calculator will evaluate your problem down to a final solution. You can also add, subtraction, multiply, and divide and complete any arithmetic you need. Step 2: Click the blue arrow to submit and see your result Big number calculator. Put a formula into the edit box (ttmath 0.9.4 prerelease): Small precision - 512 bits mantissa, 64 bits exponent Medium precision - 1024 bits mantissa, 128 bits exponent Big precision - 2048 bits mantissa, 256 bits exponent Modulo recursive problem for exponents with decimals. darkob93. EDIT: cleaned out some of the stuff from int main() to make it more readable. Hi, I have an exercise problem where I'm supposed to calculate N!modM where N! is a really big number without overflow issues. I managed to do it using ln function to output smaller numbers About Modulo Calculator . The Modulo Calculator is used to perform the modulo operation on numbers. Modulo. Given two numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder from the division of a by n.For instance, the expression 7 mod 5 would evaluate to 2 because 7 divided by 5 leaves a remainder of 2, while 10 mod 5 would evaluate to. To encrypt a message, enter valid modulus N below. Enter encryption key e and plaintext message M in the table on the left, then click the Encrypt button. The encrypted message appears in the lower box. To decrypt a message, enter valid modulus N below. Enter decryption key d and encrypted message C in the table on the right, then click the Decrypt button

mod: Calculate y modulo x, i.e. subtract (or add) x from y until the remainder is between 0 and x. Works the same for negative x. large: Large built-in font xlarge: Extra large built-in font xxlarge: the display may not be wide enough to display both numbers if you are using a large font and the numbers have large exponents This modulo calculator is used to perform modular arithmetic. The mod calculator takes two numbers and divides the second into the first. It returns a quotient and a remainder. The quotient is the greatest whole number of times the second number can be divided into the first without the remainder becoming negative Locate the ab/c button. That can be used as the mod. to calculate 29 mod 6, the display will show 29 ⌋ 6. The answer on the display is 4 ⌋ 5 ⌋ 6. 4 = quotient, 5 = remainder (the answer!), 6 = divisor. Make sure that, the divisor in the answer is the same as the divisor in the question. If they are the same, then the remainder is your.

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