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Definition. The Modulus is the remainder of the euclidean division of one number by another. % is called the modulo operation. For instance, 9 divided by 4 equals 2 but it remains 1. Here, 9 / 4 = 2 and 9 % 4 = 1. In your example: 5 divided by 7 gives 0 but it remains 5 (5 % 7 == 5). Calculation.
Note that 10^9 is also represented as 1e9. Input format One line of input containing two space separated integers, x and n. Output format Print the required answer. Sample Input 1 100000000 2. Sample Output 1 930000007. Explanation 1 (10^8)^2 = 10^16. 10^16 % (10^9+7) = 930000007. Constraints 0 <= x < 10^9. 0 <= n < 10^5.
Bill the Lizard. 404k210572888. 28. mod = a % b. This stores the result of a mod b in the variable mod. And you are right, 15 mod 4 is 3, which is exactly what python returns: >>> 15 % 4 3. a %= b is also valid. edited Jul 28, 2019 at 16:12.
Similar trick can be done for integer division by 10 where we note that we always can write a number x as x = a 10 + b, where a = x/10 and b = x%10, then again we can study x1*x2 and x1+x2 to deduce similar rules for the integer division of 128 bit integers taking advantage of the fast versions of the 64 bit ones.
10 % 3 // = 1 ; because 3 * 3 gets you 9, and 10 - 9 is 1. Apparently it is not the same as the modulo operator entirely. You can fit 3 exactly 3 times in 9. If you would add 3 one more time to 9, you would end up with 12. But you were dividing 10, so instead you say it's 3 times 9 with the remainder being 1.
0. Modulo Method First need to divide the Dividend by the Divisor: 2 4 = 0.50 Next we take the Whole part of the Quotient (0) and multiply that by the Divisor (4): 0 x 4 = 0. And finally, we take the answer in the second step and subtract it from the Dividend to get the answer to 2 mod 4: 2 - 0 = 2.
x % 2 == x & 1 Simple counterexample: x = -1. In many languages, including Java, -1 % 2 == -1. That is, % is not necessarily the traditional mathematical definition of modulo. Java calls it the "remainder operator", for example. With regards to bitwise optimization, only modulo powers of two can "easily" be done in bitwise arithmetics.
Modulus is just the remainder in division before its used in a decimal quotient. Example: The division of two numbers is often expressed as a decimal number (quotient). But the result of the division of say, 1/3, can also be expressed in whole numbers as "0 with a remainder of 1". But that form of quotient is not very helpful in modern math, so ...
As said in your question you want to find 2^100000000. It'll take "100000000" these many iterations precisely O (n). So better approach would be using modular exponentiation. Not only it calculates in O (log n) time but also gives answer in integer (long long) range by using mod 10^9+7 at intermediate steps. mod=10^9+7;
1. n3 is always odd. Exactly one of n1 and n2 is even. Exactly one of n1, n2 and n3 is divisible by 3. – Paul Hankin. Apr 9, 2017 at 13:19. 1. If your modulo is prime, and it is in the case of 10^9+7, then you can use the formula c^ (M-2) mod M to compute modular inverse of c mod M, which can be easily done with fast pow. – pkacprzak.