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