C语言求所有方程组解的总数，help！

除了十八层循环有没有更好的解法，想过用递归但却不知道怎么编 希望有人能教教我

#include<stdio.h>
#include<stdlib.h>
int a_array[18] = {57,71,87,97,99,101,103,113,114,115,128,129,131,137,147,156,163,186};
int result[18] = {0};

void recursive(int level,int sum) {
    if (17 < level) {return;}
    int i = 0 ;
    while (1) {
        int next_sum =sum - i * a_array[level];
        if (next_sum > 0 ) {
            result[level] = i;
            recursive(level + 1, next_sum);
        } else if (next_sum == 0) {
            result[level] = i;
            // int j,sum=0;
            // for(j = 0 ; j < 18 ;j++) {printf("%d*%d +",result[j],a_array[j]);sum+=result[j]*a_array[j];}
            // printf("\n%d\n",sum);
            return;
        } else {
            return;
        }
        ++i;
    }
}

int main() {
    recursive(0,1000);
}