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 fact[5003], ifact[5003];
  long long mod = 998244353;
  long long powwwer(long long i, long long j) {
    if (j == 0) return 1;
    long long w = powwwer(i, j / 2);
    w = (w * w) % mod;
    if (j % 2 == 1) {
      w = (w * i) % mod;
    }
    return w;
  }
  int main() {
    fact[0] = 1;
    ifact[0] = powwwer(fact[0], mod - 2);
    for (int i = 1; i <= 5001; i++) {
      fact[i] = (fact[i - 1] * 1LL * i) % mod;
      ifact[i] = powwwer(fact[i], mod - 2);
    }
    int n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    int cnt = 0;
    for (int i = 0; i < s.size(); i++) {
      if (s[i] == '1') cnt++;
    }
    if (cnt < k) {
      cout << 1 << endl;
      return 0;
    }
    long long ans = 1;
    for (int i = 0; i < s.size(); i++) {
      int cnt1 = 0;
      int cnt0 = 0;
      int j = i;
      while (j >= 0 && cnt1 <= k) {
        if (s[j] == '1')
          cnt1++;
        else
          cnt0++;
        j--;
      }
      if (cnt1 > k) cnt1--;
      if (s[i] == '1') {
        if (cnt0 > 0) {
          long long z = (fact[cnt1 + cnt0 - 1] * ifact[cnt0 - 1]) % mod;
          z = (z * ifact[cnt1]) % mod;
          ans = (ans + z) % mod;
        }
      } else {
        if (cnt1 > 0) {
          long long z = (fact[cnt1 + cnt0 - 1] * ifact[cnt1 - 1]) % mod;
          z = (z * ifact[cnt0]) % mod;
          ans = (ans + z) % mod;
        }
      }
    }
    cout << ans << endl;
  }
  