容斥。

总方案数 - 不合法方案数。

#include <cmath>
#include <queue>
#include <cstdio>
#include <cctype>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;

const int maxn = 100000 + 10;
int n, val[5], num[5]; long long dp[maxn], sum, ans;

inline long long Div(int x) { return 1ll * val[x] * (num[x] + 1); }

int main(int argc, char const *argv[])
{
  scanf("%d%d%d%d", val + 1, val + 2, val + 3, val + 4), scanf("%d", &n), dp[0] = 1;
  for(int k = 1; k <= 4; ++k) for(int i = 1; i < maxn; ++i) if( i - val[k] + 1 > 0 ) dp[i] = dp[i] + dp[i - val[k]];
  while( ~scanf("%d%d%d%d", num + 1, num + 2, num + 3, num + 4) ) {
    scanf("%d", &n), ans = 0;
    for(int f = 1, i = 0; i < 16; ++i) {
      sum = 0, f = 1;
      for(int j = 0; j < 4; ++j) if( (i >> j) & 1 ) sum = sum + Div(j + 1), f = -f;
      if( sum <= n ) ans = ans + f * dp[n - sum];
    }
    printf("%lld\n", ans);
  }

  return 0;
}