#include <bits/stdc++.h>
using namespace std;
int n, k, c[5100][5100];
string s;
int sum[5100];
signed main() {
  for (int i = 0; i <= 5000; i++) c[i][0] = 1;
  for (int i = 1; i <= 5000; i++)
    for (int j = 1; j <= 5000; j++) {
      c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
      if (c[i][j] >= 998244353) c[i][j] -= 998244353;
    }
  cin >> n >> k;
  cin >> s;
  s = "$" + s;
  for (int i = 1; i <= n; i++) {
    sum[i] = sum[i - 1] + (s[i] == '1');
  }
  int ans = 1;
  if (sum[n] >= k)
    for (int i = 1; i <= n; i++)
      for (int j = i + 1; j <= n; j++) {
        if (sum[j] - sum[i - 1] <= k) {
          int v1 = sum[j] - sum[i - 1], v0 = j - i + 1 - v1;
          v1 -= (s[j] == '0') + (s[i] == '0');
          v0 -= (s[j] == '1') + (s[i] == '1');
          if (v0 >= 0 && v1 >= 0) {
            ans += c[v0 + v1][v0];
            if (ans >= 998244353) ans -= 998244353;
          }
        }
      }
  cout << ans << endl;
  return 0;
}

### Prompt

In CPP, your task is to solve 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 n, k, c[5100][5100];
string s;
int sum[5100];
signed main() {
  for (int i = 0; i <= 5000; i++) c[i][0] = 1;
  for (int i = 1; i <= 5000; i++)
    for (int j = 1; j <= 5000; j++) {
      c[i][j] = c[i - 1][j] + c[i - 1][j - 1];
      if (c[i][j] >= 998244353) c[i][j] -= 998244353;
    }
  cin >> n >> k;
  cin >> s;
  s = "$" + s;
  for (int i = 1; i <= n; i++) {
    sum[i] = sum[i - 1] + (s[i] == '1');
  }
  int ans = 1;
  if (sum[n] >= k)
    for (int i = 1; i <= n; i++)
      for (int j = i + 1; j <= n; j++) {
        if (sum[j] - sum[i - 1] <= k) {
          int v1 = sum[j] - sum[i - 1], v0 = j - i + 1 - v1;
          v1 -= (s[j] == '0') + (s[i] == '0');
          v0 -= (s[j] == '1') + (s[i] == '1');
          if (v0 >= 0 && v1 >= 0) {
            ans += c[v0 + v1][v0];
            if (ans >= 998244353) ans -= 998244353;
          }
        }
      }
  cout << ans << endl;
  return 0;
}

```