/* file : countingCards.c */
/* author : Oscar Miró (o.miro.i.lopez.feliu@student.rug.nl) */
 
/* Description:
 *
 */

#include <stdio.h>

// func checks if an array is sorted in ascending order. Returns false if arr[n] > arr[n+1]
// returns true if its either ascending or they have the same value
int isAscending (int size, int arr[]) {

    for (int i = 0; i < size - 1; i++) {
        if (arr[i] > arr[i+1]) {
            return 0;
        }
    }
    return 1;
}

// main recursive function
int check (int size, int dist[], int type, int found, int arr[]) {

    // checks if the hand passed is full
    if (found == size) {
        // checks if the hand is unique. For every combination of cards, say ABC, ACB BCA,
        // if you only consider the ones that are in ascending order you avoid repeating it
        if (isAscending(size, arr)) {
            return 1;
        }
        // if hand not not ascending, looks for another hand
        return 0;
    } 
    
    else if (!isAscending(found, arr)) {
        return 0;
    }

    // if the hand is not full add another card

    int count = 0;

    // iterates for every card type, adds a card
    for (int i = 0; i < type; i++) {

        // checks that in the card distribution there are enough cards to add one
        if (dist[i] > 0) {

            arr[found] = i;

            // removes a one from the type of card added when passing it
            dist[i]--;

            // recalls func. adds another card till hand is full, then returns 1 if 
            // hand is unique. 1 is added to count, when all combinations are checked 
            // returns count which is later output
            count += check (size, dist, type, found+1, arr);

            // adds it again after passing it, for other iterations
            dist[i]++;  
        }
    }

    return count;
}

int main (int argc, char *argv[]) {

    // declaration and scanning
    int size, type, arr[10000], found = 0;

    scanf("%d %d", &size, &type);

    // arr dist holds the number of cards for each type
    int dist[type];

    for (int i = 0; i < type; i++) {
        scanf("%d", dist + i);
    }

    // finds the combination of cards
    printf("%d\n", check(size, dist, type, found, arr));
}