Smallest count

You are given $n$ coin values and a sum $x$. How many ways can you choose the coins so that they sum up to $x$ and so that the number of coins is the smallest possible?

You may assume that $1 \le n \le 10$ and that $1 \le x \le 100$. One of the coin values is always $1$. The algorithm should be efficient in all these cases.

In a file minways.py, implement a function count that returns the desired count.

def count(x, coins):
    # TODO

if __name__ == "__main__":
    print(count(5, [1])) # 1
    print(count(5, [1, 2, 3, 4])) # 4
    print(count(13, [1, 2, 5])) # 12
    print(count(42, [1, 5, 6, 17])) # 30

Explanation: When $x=5$ and the coin values are $[1,2,3,4]$, there are $4$ different ways: $[1,4]$, $[2,3]$, $[3,2]$ and $[4,1]$.