#include <bits/stdc++.h>
using namespace std;
int c[5001][5001];
int main() {
  for (int i = 0; i <= 5000; i++) {
    for (int j = 0; j <= i; j++) {
      if (j == 0)
        c[i][j] = 1;
      else
        c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
      c[i][j] %= 998244353LL;
    }
  }
  int n, k;
  string s;
  cin >> n >> k >> s;
  if (k == 0) {
    cout << "1\n";
    return 0;
  }
  long long int ans = 1LL, cnt = 0, pos = 0;
  bool first = 1;
  for (int i = 0; i < n; i++) {
    if (s[i] == '1') cnt++;
    if (cnt < k) continue;
    while (cnt != k && pos <= i) {
      pos++;
      if (s[pos - 1] == '1') cnt--;
    }
    int len = i - pos + 1;
    if (first) {
      ans += c[len][cnt] - 1;
    } else if (s[i] == '1') {
      ans += c[len - 1][cnt];
    } else {
      ans += c[len - 1][cnt - 1];
    }
    first = 0;
    ans %= 998244353LL;
  }
  cout << ans << '\n';
}

### Prompt

Your task is to create a cpp solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int c[5001][5001];
int main() {
  for (int i = 0; i <= 5000; i++) {
    for (int j = 0; j <= i; j++) {
      if (j == 0)
        c[i][j] = 1;
      else
        c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
      c[i][j] %= 998244353LL;
    }
  }
  int n, k;
  string s;
  cin >> n >> k >> s;
  if (k == 0) {
    cout << "1\n";
    return 0;
  }
  long long int ans = 1LL, cnt = 0, pos = 0;
  bool first = 1;
  for (int i = 0; i < n; i++) {
    if (s[i] == '1') cnt++;
    if (cnt < k) continue;
    while (cnt != k && pos <= i) {
      pos++;
      if (s[pos - 1] == '1') cnt--;
    }
    int len = i - pos + 1;
    if (first) {
      ans += c[len][cnt] - 1;
    } else if (s[i] == '1') {
      ans += c[len - 1][cnt];
    } else {
      ans += c[len - 1][cnt - 1];
    }
    first = 0;
    ans %= 998244353LL;
  }
  cout << ans << '\n';
}

```