#include <bits/stdc++.h>
using namespace std;
long long mod = 998244353;
long long c[5005][5005];
void get_c() {
  c[0][0] = 1;
  for (int i = 1; i <= 5000; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++)
      c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
    for (int j = i + 1; j <= 5000; j++) c[i][j] = 0;
  }
}
int a[5005];
int main() {
  get_c();
  a[0] = 0;
  int nnow = 0;
  int n, k;
  long long ans = 1;
  cin >> n >> k;
  string s;
  cin >> s;
  int i = 0;
  while (i < n) {
    if (s[i] == '1') {
      nnow++;
      a[nnow] = i + 1;
    }
    if (nnow == k && s[i] == '1') {
      ans = (ans - 1 + c[i + 1][nnow]) % mod;
    } else if (nnow >= k) {
      int l = a[nnow - k] + 1;
      int r = i + 1;
      int tt = k - 1;
      if (s[i] == '1') {
        tt++;
      }
      if (r - l >= 0) ans = (ans + c[r - l][tt]) % mod;
    }
    i++;
  }
  ans = ans % mod;
  cout << ans << endl;
  return 0;
}

### 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;
long long mod = 998244353;
long long c[5005][5005];
void get_c() {
  c[0][0] = 1;
  for (int i = 1; i <= 5000; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++)
      c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
    for (int j = i + 1; j <= 5000; j++) c[i][j] = 0;
  }
}
int a[5005];
int main() {
  get_c();
  a[0] = 0;
  int nnow = 0;
  int n, k;
  long long ans = 1;
  cin >> n >> k;
  string s;
  cin >> s;
  int i = 0;
  while (i < n) {
    if (s[i] == '1') {
      nnow++;
      a[nnow] = i + 1;
    }
    if (nnow == k && s[i] == '1') {
      ans = (ans - 1 + c[i + 1][nnow]) % mod;
    } else if (nnow >= k) {
      int l = a[nnow - k] + 1;
      int r = i + 1;
      int tt = k - 1;
      if (s[i] == '1') {
        tt++;
      }
      if (r - l >= 0) ans = (ans + c[r - l][tt]) % mod;
    }
    i++;
  }
  ans = ans % mod;
  cout << ans << endl;
  return 0;
}

```