description: You are given a binary string (i. e. a string consisting of characters 0 and/or 1) s of length n. You can perform the following operation with the string s at most once: choose a substring (a contiguous subsequence) of s having exactly k characters 1 in it, and shuffle it (reorder the characters in the substring as you wish).
  
  Calculate the number of different strings which can be obtained from s by performing this operation at most once.
  
  Input
  
  The first line contains two integers n and k (2 ≤ n ≤ 5000; 0 ≤ k ≤ n).
  
  The second line contains the string s of length n, consisting of characters 0 and/or 1.
  
  Output
  
  Print one integer — the number of different strings which can be obtained from s by performing the described operation at most once. Since the answer can be large, output it modulo 998244353.
  
  Examples
  
  Input
  
  
  7 2
  1100110
  
  
  Output
  
  
  16
  
  
  Input
  
  
  5 0
  10010
  
  
  Output
  
  
  1
  
  
  Input
  
  
  8 1
  10001000
  
  
  Output
  
  
  10
  
  
  Input
  
  
  10 8
  0010011000
  
  
  Output
  
  
  1
  
  Note
  
  Some strings you can obtain in the first example:
  
    * to obtain 0110110, you can take the substring from the 1-st character to the 4-th character, which is 1100, and reorder its characters to get 0110; 
    * to obtain 1111000, you can take the substring from the 3-rd character to the 7-th character, which is 00110, and reorder its characters to get 11000; 
    * to obtain 1100101, you can take the substring from the 5-th character to the 7-th character, which is 110, and reorder its characters to get 101. 
  
  
  
  In the second example, k = 0 so you can only choose the substrings consisting only of 0 characters. Reordering them doesn't change the string at all, so the only string you can obtain is 10010.
solution: #include <bits/stdc++.h>
  using namespace std;
  int n, k, c[5100][5100];
  string s;
  int sum[5100];
  signed main() {
    for (int i = 0; i <= 5000; i++) c[i][0] = 1;
    for (int i = 1; i <= 5000; i++)
      for (int j = 1; j <= 5000; j++) {
        c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
        if (c[i][j] >= 998244353) c[i][j] -= 998244353;
      }
    cin >> n >> k;
    cin >> s;
    s = "$" + s;
    for (int i = 1; i <= n; i++) {
      sum[i] = sum[i - 1] + (s[i] == '1');
    }
    int ans = 1;
    if (sum[n] >= k)
      for (int i = 1; i <= n; i++)
        for (int j = i + 1; j <= n; j++) {
          if (sum[j] - sum[i - 1] <= k) {
            int v1 = sum[j] - sum[i - 1], v0 = j - i + 1 - v1;
            v1 -= (s[j] == '0') + (s[i] == '0');
            v0 -= (s[j] == '1') + (s[i] == '1');
            if (v0 >= 0 && v1 >= 0) {
              ans += c[v0 + v1][v0];
              if (ans >= 998244353) ans -= 998244353;
            }
          }
        }
    cout << ans << endl;
    return 0;
  }
  