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;
  const int N = 2e5 + 9, inf = 0x3f3f3f3f, mod = 998244353;
  long long C[5010][5010];
  void solve() {
    for (int i = 0; i <= 5000; i++) {
      C[i][0] = 1;
      for (int j = 1; j <= i; j++) {
        C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % mod;
      }
    }
    long long n, k;
    scanf("%lld%lld", &n, &k);
    string s;
    cin >> s;
    int lo = 0, ri = 0, cnt = 0, plo = -inf, pri = -inf;
    long long ans = 0;
    if (k == 0) {
      printf("1\n");
      return;
    }
    while (ri < n) {
      if (s[ri] == '1') cnt++;
      while (ri + 1 < n && s[ri + 1] == '0') ri++;
      while (cnt > k) {
        if (s[lo] == '1') cnt--;
        lo++;
      }
      if (cnt == k) {
        ans = (ans + C[ri - lo + 1][k]) % mod;
        if (plo != -inf) {
          ans = (ans - C[pri - lo + 1][k - 1] + mod) % mod;
        }
        plo = lo;
        pri = ri;
      }
      ri++;
    }
    if (pri == -inf) {
      printf("1\n");
      return;
    }
    printf("%lld\n", (ans + mod) % mod);
  }
  int main() {
    solve();
    return 0;
  }
  