Polynomial coefficients 

The Problem

The problem is to calculate the coefficients in expansion of polynomial (x1+x2+...+xk)n.

The Input

The input will consist of a set of pairs of lines. The first line of the pair consists of two integers n and k separated with space (0<K,N<13). This integers define the power of the polynomial and the amount of the variables. The second line in each pair consists of k non-negative integers n1, ..., nk, where n1+...+nk=n.

The Output

For each input pair of lines the output line should consist one integer, the coefficient by the monomial x1n1x2n2...xknk in expansion of the polynomial (x1+x2+...+xk)n.

Sample Input

2 2
1 1
2 12
1 0 0 0 0 0 0 0 0 0 1 0

Sample Output