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;
  void judge() {}
  const int MOD = 998244353;
  int add(int x, int y) {
    x += y;
    while (x >= MOD) x -= MOD;
    while (x < 0) x += MOD;
    return x;
  }
  int main() {
    judge();
    int n;
    cin >> n;
    int k;
    cin >> k;
    string s;
    cin >> s;
    vector<int> p(n + 1);
    for (int i = 0; i < n; i++) p[i + 1] = p[i] + (s[i] - '0');
    vector<vector<int>> C(n + 1);
    for (int i = 0; i <= n; i++) {
      C[i].resize(i + 1);
      C[i][0] = C[i][i] = 1;
      for (int j = 1; j < i; j++) C[i][j] = add(C[i - 1][j], C[i - 1][j - 1]);
    }
    int ans = 1;
    for (int i = 0; i < n; i++)
      for (int j = i + 1; j < n; j++) {
        int cnt = j + 1 - i;
        int cnt1 = p[j + 1] - p[i];
        if (cnt1 > k || p[n] < k) continue;
        cnt -= 2;
        if (s[i] == '0') cnt1--;
        if (s[j] == '0') cnt1--;
        if (cnt1 <= cnt && cnt1 >= 0 && cnt >= 0) ans = add(ans, C[cnt][cnt1]);
      }
    cout << ans << endl;
    return 0;
  }
  