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Power and Mod

Limits: 1.5s, 512 MB

Exponentiation is a mathematical operation, written as b n , involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases:

bn = b × … × b (n times)

In computing, the modulo operation finds the remainder after division of one number by another (sometimes called modulus). Given two positive numbers, a (the dividend) and n (the divisor), a modulo n (abbreviated as a mod n) is the remainder of the Euclidean division of a by n. For instance, the expression “5 mod 2” would evaluate to 1 because 5 divided by 2 leaves a quotient of 2 and a remainder of 1, while “9 mod 3” would evaluate to 0 because the division of 9 by 3 has a quotient of 3 and leaves a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3.

Now, you are given the value of a, b and m. print the value of

ab mod m

Input

First line contains the number of test cases T (1 <= T <= 10^4). Next T line contains three integers a, b and m (1 <= a, b <=10^9 and 1 <= m <= 2^64).

Output

For each test case print the answer of the problem.

Samples

InputOutput
2
2 3 4
3 4 5
0
1

This problem was authored for Inter Department Programming Contest 2016 at Jahangirnagar University and is being hosted on Toph per author’s request.

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