Problem Statement

Sereja has a sequence of n integers a[1], a[2], ..., a[n]. Sereja can do following transformation of the array:

create a new sequence of n integers b[1], b[2], ..., b[n]in this way: (1 ≤ i ≤ n)

Replace the sequence a by b, i.e., a[i] = b[i] for all i in [1, n]

Sereja decided to use his transformation k times. Then he computed the value of , where r — the sequence obtained after k transformations of sequence a, as described above.

Sereja lost sequence a, but he was left with the numbers q(r) and k. Now Sereja is interested in the question : what is the number of the sequences of the integers с[1], с[2], ..., с[n], such that 1 ≤ c[i] ≤ m and q(d) = q(r), where d — the sequence obtained after k transformations of sequence c, as described above.

Input

The first lines contains a single integer T, denoting the number of test cases. Each test case consist of four integers : n, m, q(r), k.

Output

In a single line print the remainder of division the answer of the problem on number 10^9 + 7.

Constraints

1 ≤ T ≤ 10000
1 ≤ n, m, q(r), k ≤ 10^9

Example
Input:
3
1 1 1 1
2 2 1 1
2 3 1 1

Output:
0
2
4

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