In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, which computes, besides the greatest common divisor of integers a and b, the coefficients of Bézout's identity, that is integers x and y such that ax + by = gcd(a, b).
---Wikipedia
Today, ex-Euclid takes revenge on you. You need to calculate how many distinct positive pairs of (x, y) such as ax + by = c for given a, b and c.
The first line contains a single integer T, indicating the number of test cases.
Each test case only contains three integers a, b and c.
[Technical Specification]
1. 1 <= T <= 100
2. 1 <= a, b, c <= 1 000 000
For each test case, output the number of valid pairs.