Problem Description

A thief made his way to a shop.

There are \(n\) kinds of products in the shop and an infinite number of products of each kind. The value of one product of kind \(i\) is \(a_i\).

The thief wonders how many way to take some products such that the value of them is exactly \(k\) (it's possible for some kinds to take several products of that kind).

Find the answer modulo \(10^9 +7\).

Input

The first line of the input gives the number of test cases, \(T(1\le T\le 100)\). \(T\) test cases follow.

For each test case, the first line contains two integers \(n, k(1\le n\le 100,1\le k\le 10^{18})\), the number of kinds of products and the value of products the thief will take.

The second line contains \(n\) integers \(a_i (1\le a_i\le 10)\) — the values of products for kinds from \(1\) to \(n\).

It is guaranteed that there are no more than 10 testcases with \(n>50\).

It is guaranteed that there are no more than 40 testcases with \(n>20\).

It is guaranteed that there are no more than 80 testcases with \(n>10\).

Output

For each test case, print a line with an integer, representing the answer, modulo \(10^9+7\).

5
4 10
1 2 5 10
4 100
1 2 5 10
5 20
1 1 1 1 1
10 1000000000000
1 2 3 4 5 6 7 8 9 10
20 1000000000000000000
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

11
2156
10626
321553432
822368450