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>
  const long long mod = 998244353;
  const int maxn = 1023 * 5;
  long long qpow[maxn];
  long long inv_qpow[maxn];
  int get_inv(int val) {
    int nume = mod - 2;
    int ans = 1;
    while (nume) {
      if (nume & 1) {
        ans = 1ll * val * ans % mod;
      }
      val = 1ll * val * val % mod;
      nume >>= 1;
    }
    return ans;
  }
  void init_data() {
    qpow[0] = 1;
    for (int i = 1; i < maxn; i++) {
      qpow[i] = 1ll * qpow[i - 1] * i % mod;
    }
    inv_qpow[maxn - 1] = get_inv(qpow[maxn - 1]);
    for (int i = maxn - 1; i > 0; i--) {
      inv_qpow[i - 1] = 1ll * inv_qpow[i] * i % mod;
    }
  }
  int get_C(int m, int n) {
    if (m < n) {
      return 0;
    }
    long long ans = 1;
    ans = qpow[m] * inv_qpow[n] % mod;
    ans = ans * inv_qpow[m - n] % mod;
    return ans;
  }
  char char_s[maxn];
  int rec_num[maxn];
  int main() {
    init_data();
    int n, k;
    scanf("%d%d", &n, &k);
    scanf("%s", char_s);
    if (k == 0) {
      printf("1\n");
      return 0;
    }
    rec_num[0] = (char_s[0] == '1');
    for (int i = 1; i < n; i++) {
      rec_num[i] = (char_s[i] == '1') + rec_num[i - 1];
    }
    if (rec_num[n - 1] < k) {
      printf("1\n");
      return 0;
    }
    long long ans = 0;
    for (int left_ = 0; left_ < n; left_++) {
      int last_num = left_ == 0 ? 0 : rec_num[left_ - 1];
      int right_ =
          std::upper_bound(rec_num, rec_num + n, last_num + k) - rec_num - 1;
      if (rec_num[right_] - last_num < k) {
        break;
      }
      int len_ = right_ - left_ + 1;
      if (char_s[left_] == '0') {
        ans = (ans + get_C(len_ - 1, k - 1)) % mod;
      } else {
        ans = (ans + get_C(len_ - 1, k)) % mod;
        if (right_ == n - 1) {
          ans = (ans + get_C(len_ - 1, k - 1)) % mod;
        }
      }
    }
    printf("%lld\n", ans);
  }
  