Counting Coin Combinations

Given several coin denominations and a target amount, count how many distinct combinations of coins can make that amount.

Each denomination may be used any number of times. Two ways that differ only by the order of the coins are considered the same combination.

The first line contains the number of test cases T.

Each test case consists of three lines.

• The first line contains the number of coin denominations N (1 <= N <= 20).
• The second line contains the N coin values in increasing order. Each value is an integer from 1 to 10000.
• The third line contains the target amount M (1 <= M <= 10000).

You may assume that the number of combinations is less than $2^{31}-1$.

For each test case, print one line containing the number of combinations that make amount M using the given denominations.