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 = 1000001;
  long long factinverse[N + 1], inverse[N + 1], fact[N + 1];
  long long binomial(long long N, long long R) {
    return (R > N) ? 0
                   : fact[N] * factinverse[R] % 998244353 * factinverse[N - R] %
                         998244353;
  }
  void precompute() {
    inverse[0] = inverse[1] = 1;
    for (int i = 2; i <= N; i++)
      inverse[i] =
          inverse[998244353 % i] * (998244353 - 998244353 / i) % 998244353;
    factinverse[0] = factinverse[1] = 1;
    for (int i = 2; i <= N; i++)
      factinverse[i] = inverse[i] * factinverse[i - 1] % 998244353;
    fact[0] = 1;
    for (int i = 1; i <= N; i++) fact[i] = fact[i - 1] * i % 998244353;
  }
  int main() {
    cin.tie(0)->sync_with_stdio(0);
    precompute();
    long long n, k;
    string str;
    cin >> n >> k >> str;
    if (k == 0) {
      cout << "1\n";
      return 0;
    }
    int left = 0;
    int right = -1;
    int onecount = 0;
    while (onecount != k && right + 1 < n) {
      if (str[right + 1] == '1') {
        onecount++;
      }
      right++;
    }
    if (onecount != k) {
      cout << "1\n";
      return 0;
    }
    while (right + 1 < n && str[right + 1] == '0') {
      right++;
    }
    long long ans = 0;
    ans = binomial(right - left + 1, k);
    while (left < n && right < n) {
      while (left < n && onecount == k) {
        if (str[left] == '1') {
          onecount--;
        }
        left++;
      }
      if (left == n) break;
      while (onecount != k && right + 1 < n) {
        if (str[right + 1] == '1') {
          onecount++;
        }
        right++;
      }
      if (onecount != k) break;
      while (right + 1 < n && str[right + 1] == '0') {
        right++;
      }
      int flag = 0;
      for (int i = right; i >= left + k - 2; i--) {
        if (str[i] == '1' && !flag) {
          flag = 1;
          continue;
        }
        ans += binomial(i - left, k - 1);
        ans %= 998244353;
      }
    }
    cout << ans << "\n";
  }
  