#include <bits/stdc++.h>
using namespace std;
void judge() {}
const int MOD = 998244353;
int add(int x, int y) {
  x += y;
  while (x >= MOD) x -= MOD;
  while (x < 0) x += MOD;
  return x;
}
int main() {
  judge();
  int n;
  cin >> n;
  int k;
  cin >> k;
  string s;
  cin >> s;
  vector<int> p(n + 1);
  for (int i = 0; i < n; i++) p[i + 1] = p[i] + (s[i] - '0');
  vector<vector<int>> C(n + 1);
  for (int i = 0; i <= n; i++) {
    C[i].resize(i + 1);
    C[i][0] = C[i][i] = 1;
    for (int j = 1; j < i; j++) C[i][j] = add(C[i - 1][j], C[i - 1][j - 1]);
  }
  int ans = 1;
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++) {
      int cnt = j + 1 - i;
      int cnt1 = p[j + 1] - p[i];
      if (cnt1 > k || p[n] < k) continue;
      cnt -= 2;
      if (s[i] == '0') cnt1--;
      if (s[j] == '0') cnt1--;
      if (cnt1 <= cnt && cnt1 >= 0 && cnt >= 0) ans = add(ans, C[cnt][cnt1]);
    }
  cout << ans << endl;
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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;
void judge() {}
const int MOD = 998244353;
int add(int x, int y) {
  x += y;
  while (x >= MOD) x -= MOD;
  while (x < 0) x += MOD;
  return x;
}
int main() {
  judge();
  int n;
  cin >> n;
  int k;
  cin >> k;
  string s;
  cin >> s;
  vector<int> p(n + 1);
  for (int i = 0; i < n; i++) p[i + 1] = p[i] + (s[i] - '0');
  vector<vector<int>> C(n + 1);
  for (int i = 0; i <= n; i++) {
    C[i].resize(i + 1);
    C[i][0] = C[i][i] = 1;
    for (int j = 1; j < i; j++) C[i][j] = add(C[i - 1][j], C[i - 1][j - 1]);
  }
  int ans = 1;
  for (int i = 0; i < n; i++)
    for (int j = i + 1; j < n; j++) {
      int cnt = j + 1 - i;
      int cnt1 = p[j + 1] - p[i];
      if (cnt1 > k || p[n] < k) continue;
      cnt -= 2;
      if (s[i] == '0') cnt1--;
      if (s[j] == '0') cnt1--;
      if (cnt1 <= cnt && cnt1 >= 0 && cnt >= 0) ans = add(ans, C[cnt][cnt1]);
    }
  cout << ans << endl;
  return 0;
}

```