Another thief in a Shop

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).

Sample Input

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

Sample Output

11

2156

10626

321553432

822368450

Source

2021“MINIEYE杯”中国大学生算法设计超级联赛（1）