A flea market stall has n items for sale, each with a positive integer price; several items may share the same price. A shopper wants to select a bundle of items (each item used at most once) whose prices sum to exactly T.
Two bundles are considered the same deal if they use the same multiset of prices, regardless of which specific items produce those prices. Count the number of distinct deals summing to exactly T. The empty bundle sums to 0.
Input format
Line 1: two integers n and T.
Line 2: n space-separated positive integers, the item prices (may repeat).
Output format
A single integer: the number of distinct price-multisets summing to exactly T.
Constraints
- 1 <= n <= 16
- 1 <= each price <= 100
- 0 <= T <= 1600