Problem B
Five, Six, Pick Up Sticks; Seven, Eight, Lay Them Straight

Image by denvie balidoy.

You and your friend are playing a game involving sticks of different lengths. Your opponent picks the sticks you will receive, and a number $n$. He then challenges you to lay some of the sticks down end-to-end in a straight line, so that the total length of all the sticks you’ve laid down is exactly a positive multiple of $n$. Being tired of working so hard at challenges which aren’t solvable, you’ve decided to write a program to at least determine if a challenge can be solved, before you spend a lot of time trying to solve it yourself.

Input

Input consists of up to $100$ challenges, one per line. Each challenge begins with two integers $n$ and $m$, where $2 \le n \le 400$ and $2 \le m \le 100$ is the number of sticks. This is followed by the lengths of the $m$ sticks; each length is an integer in the range $[1,n-1]$. Input ends when $n$ and $m$ are both zero.

Output

For each challenge, print out ‘yes’ if it is possible to solve the challenge, or ‘no’ otherwise. If it’s possible, print out the shortest length of sticks you must lay to solve the challenge.

5 3 1 2 4
5 2 2 2
5 5 4 4 4 4 4
5 5 4 4 4 4 3
0 0

yes 5
no
yes 20
yes 15