Algorithm title: UVA 10105 polynomial coefficients (number theory)

Polynomial coefficients

The Problem

The problem is to calculate the coefficients in expansion of polynomial (X1+X2+...+XK) n.

The Input

The input would consist of a set of pairs of lines. The the pair consists of two integers n andk separated with spaces (0<k,n<13). This is 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 monomialx1n1x2n2...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

2

2