Description
There are many types and sizes of smart bricks; all of them will automatically link together when touching. Given N types of bricks where each brick i has length Li , how many ways are there to lay them in a line with total length Ltotal ?
Input Format
The first line of the input provides T, the total number of test cases.
The next T pairs of lines describe a single test case:
The first line in a test case privides the number of brick types (N) and the total target length ( Ltotal ).
The second line has N values, each indicating the length of each available brick.
Constraints
1 ≤ T ≤ 10
1 ≤ N ≤ 50
1 ≤ Ltotal ≤ 106
1 ≤ Li ≤ 106
Output Format
T lines, one per test case, each indicating the number of combinations possible to make a line of that total length. Some of the values are quite large, so mod your answer by 1000000009.
Example 0
Sample Input
2
2 5
1 2
2 7
1 3
Sample Output
8
9a
