Q10105: Polynomial coefficients

// Run time: 0.010
#include <stdio.h>
int arr[12];
double calculate(int n, int m);

int main()
{
    int n, k;
    int i;
    double prod;
    int sum;
    while (scanf("%d%d", &n, &k) == 2)
    {
        prod = 1;
        sum = 0;
        for ( i = 0; i < k; i++)
            scanf("%d", &arr[i]);

        for ( i = 0; i < k; i++)
            sum += arr[i];

        if (sum > n)
        {
            printf("0\n");
            continue;
        }
        for ( i = 0; i < k; i++)
        {
            prod *= calculate(n, arr[i]);
            n -= arr[i];
        }
        printf("%.0lf\n", prod);

    }

    return 0;
}

double calculate(int n, int m)
{
    int i, j;
    double sum = 1;

    if (2*m > n)
        m = n-m;

    for ( i = 0; i < m;)
        sum *= double(n--)/double(++i);

    return sum;
}