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.
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.
1. 1 ≤ T ≤ 10
2. 1 ≤ A, B, C ≤ 109
3. 1 ≤ N ≤ 103
Input: 2 1 3 4 1 1 3 4 2 Output: 333333336 444444447
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