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;
  mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
  const int MOD = 1000000007;
  const int MOD2 = 998244353;
  using namespace std;
  void setIn(string s) { freopen(s.c_str(), "r", stdin); }
  void setOut(string s) { freopen(s.c_str(), "w", stdout); }
  void usaco(const string &USACO_TAG) {
    setIn(USACO_TAG + ".in");
    setOut(USACO_TAG + ".out");
  }
  const bool MULTIPLE_TEST_CASE = false;
  const int MAXN = 5e3 + 5;
  long long dp[MAXN][MAXN];
  void pre() {
    for (int i = 1; i < MAXN; i++) {
      dp[i][0] = 1;
      dp[i][i] = 1;
    }
    for (int i = 1; i < MAXN; i++) {
      for (int j = 1; j <= i; j++) {
        if (i == j) continue;
        dp[i][j] = dp[i - 1][j] + dp[i - 1][j - 1];
        if (dp[i][j] >= MOD2) dp[i][j] %= MOD2;
      }
    }
  }
  long long nck(int n, int k) {
    if (n == k || k == 0) {
      return 1;
    }
    return dp[n][k];
  }
  void run_case() {
    pre();
    int n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    vector<int> cum(n + 1, 0);
    for (int i = 1; i <= n; i++) {
      cum[i] = cum[i - 1] + (s[i - 1] == '1');
    }
    bool f = 0;
    long long ans = 1;
    for (int i = 1; i <= n; i++) {
      for (int j = i + 1; j <= n; j++) {
        if (cum[j] - cum[i - 1] == k) f = 1;
      }
    }
    if (!f) {
      cout << 1;
      exit(0);
      ;
    }
    for (int i = 1; i <= n; i++) {
      for (int j = i + 1; j <= n; j++) {
        if (cum[j] - cum[i - 1] <= k) {
          int ones = cum[j] - cum[i - 1];
          if (s[i - 1] == '0') ones--;
          if (s[j - 1] == '0') ones--;
          int nn = j - i - 1;
          if (nn < 0 || nn < ones || ones < 0) continue;
          ans = ans + nck(nn, ones);
          if (ans >= MOD2) ans %= MOD2;
        }
      }
    }
    cout << ans << endl;
  }
  int main() {
    cin.tie(0);
    cin.sync_with_stdio(false);
    ;
    int t;
    if (MULTIPLE_TEST_CASE)
      cin >> t;
    else
      t = 1;
    while (t--) run_case();
  }
  