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Problems > Counting Coin Combinations

Counting Coin Combinations

Difficulty: 1500 3000 ms 128 MB

dp

With unlimited coins of the given denominations, count the combinations (order does not matter) summing exactly to T, modulo 109+7.

Input: the first line has N and T; the second line has the N denominations.

Output: the number of combinations mod 109+7.

Constraints:

  • 1 ≤ N ≤ 12
  • 0 ≤ T ≤ 104
  • 1 ≤ ci ≤ 100

Sample Tests

Input 1
3 5
1 2 5
Output 1
4
Input 2
1 4
3
Output 2
0

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