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;
  long long mod = 998244353;
  long long c[5005][5005];
  void get_c() {
    c[0][0] = 1;
    for (int i = 1; i <= 5000; i++) {
      c[i][0] = 1;
      for (int j = 1; j <= i; j++)
        c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
      for (int j = i + 1; j <= 5000; j++) c[i][j] = 0;
    }
  }
  int a[5005];
  int main() {
    get_c();
    a[0] = 0;
    int nnow = 0;
    int n, k;
    long long ans = 1;
    cin >> n >> k;
    string s;
    cin >> s;
    int i = 0;
    while (i < n) {
      if (s[i] == '1') {
        nnow++;
        a[nnow] = i + 1;
      }
      if (nnow == k && s[i] == '1') {
        ans = (ans - 1 + c[i + 1][nnow]) % mod;
      } else if (nnow >= k) {
        int l = a[nnow - k] + 1;
        int r = i + 1;
        int tt = k - 1;
        if (s[i] == '1') {
          tt++;
        }
        if (r - l >= 0) ans = (ans + c[r - l][tt]) % mod;
      }
      i++;
    }
    ans = ans % mod;
    cout << ans << endl;
    return 0;
  }
  