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 c[5001][5001];
  int main() {
    for (int i = 0; i <= 5000; i++) {
      for (int j = 0; j <= i; j++) {
        if (j == 0)
          c[i][j] = 1;
        else
          c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
        c[i][j] %= 998244353LL;
      }
    }
    int n, k;
    string s;
    cin >> n >> k >> s;
    if (k == 0) {
      cout << "1\n";
      return 0;
    }
    long long int ans = 1LL, cnt = 0, pos = 0;
    bool first = 1;
    for (int i = 0; i < n; i++) {
      if (s[i] == '1') cnt++;
      if (cnt < k) continue;
      while (cnt != k && pos <= i) {
        pos++;
        if (s[pos - 1] == '1') cnt--;
      }
      int len = i - pos + 1;
      if (first) {
        ans += c[len][cnt] - 1;
      } else if (s[i] == '1') {
        ans += c[len - 1][cnt];
      } else {
        ans += c[len - 1][cnt - 1];
      }
      first = 0;
      ans %= 998244353LL;
    }
    cout << ans << '\n';
  }
  