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Division II
Easy Accuracy: 39.67% Submissions: 58 Points: 2

You were late in the maths class which is taught by Geek. Now to punish you, Geek gave you a problem to solve. Given four integer numbers A, B, C, and N, Geek wants you to find f(f(..........f(a))) N times. Where f(x) = ((x/b) * c) - 1.
Output can be represented as a fraction P/Q, you have to output P*Q-1 modulo 109 + 7, where Q-1 is modular multiplicative inverse of Q modulus 109 + 7.

Input:
1. The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
2. The first line of each test case contains four space-separated integers A, B, C, and N.

Output: For each test case, print the answer.

Constraints:
1. 1 ≤  T ≤ 10

2. 1 ≤  A, B, C ≤  109
3. 1 ≤  N ≤  103

Example:

Input:
2
1 3 4 1
1 3 4 2
Output:
333333336
444444447