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 int modulo(long long int a, long long int b) {
    long long total = 1;
    while (b > 0) {
      if (b & 1) {
        total = (total * a) % 998244353;
      }
      a = (a * a) % 998244353;
      b >>= 1;
    }
    return total;
  }
  vector<long long int> factorial(1, 1);
  vector<long long int> inversoFactorial(1, 1);
  long long int y(int n, int k) {
    if (k < 0 || k > n) {
      return 0;
    }
    while (factorial.size() < n + 1) {
      factorial.push_back(factorial.back() * factorial.size() % 998244353);
      inversoFactorial.push_back(modulo(factorial.back(), 998244351));
    }
    return (factorial[n] * inversoFactorial[k] % 998244353) *
           inversoFactorial[n - k] % 998244353;
  }
  int main() {
    ios_base::sync_with_stdio(0);
    cout.tie();
    cin.tie();
    int a, b;
    cin >> a >> b;
    string temp;
    cin >> temp;
    int lista[a];
    for (int i = 0; i < a; ++i) {
      lista[i] = temp[i] - 48;
    }
    int contar[a + 1];
    contar[0] = 0;
    for (int i = 0; i < a; ++i) {
      contar[i + 1] = contar[i] + lista[i];
    }
    long long int total = 1;
    if (contar[a] >= b) {
      for (int i = 0; i < a; ++i) {
        for (int j = i + 1; j < a; ++j) {
          int z = contar[j + 1] - contar[i];
          if (z <= b) {
            z -= (lista[i] ^ 1) + (lista[j] ^ 1);
            int x = j - i - 1;
            total += y(x, z);
            total %= 998244353;
          }
        }
      }
    }
    cout << total << ' ';
  }
  