An apothecary stocks vials of several distinct integer strengths, with an unlimited supply of each strength. A dose is prepared by pouring some vials together; only the multiset of strengths used matters, not the order in which they are poured.
Count how many distinct multisets of vials have strengths summing exactly to the target dose T. The empty multiset sums to 0.
Input format
Line 1: two integers n and T.
Line 2: n space-separated distinct positive integers, the available vial strengths.
Output format
A single integer: the number of distinct multisets of vials summing to exactly T.
Constraints
- 1 <= n <= 12
- 1 <= each strength <= 30, all strengths distinct
- 0 <= T <= 300