Coin Combinations

Statement

You have n different coin values and may use each value any number of times. Count the number of distinct combinations of coins whose total is exactly T. Two combinations are the same if they use each value the same number of times, whatever the order. Print the count modulo 1000000007.

Input

The first line has n and T. The second line has the n coin values.

Output

Print one integer: the number of combinations modulo 1000000007.

Constraints

1 <= n <= 100
0 <= T <= 10000
1 <= coin value <= 10000, all values distinct

Example 1

3 5
1 2 5

4

The combinations are 5; 2+2+1; 2+1+1+1; and 1+1+1+1+1.

Example 2

1 3
2

0

Three cannot be made from 2s.