#include <bits/stdc++.h>
using namespace std;
long long int inf = 998244353;
long long int facto[1000010];
long long int power(long long int a, long long int pow) {
  long long int ans = 1;
  if (a < 0) a += inf;
  while (pow) {
    if (pow % 2 == 1) {
      ans = ((ans % inf) * (a % inf)) % inf;
    }
    a = ((a % inf) * (a % inf)) % inf;
    if (a < 0) a += inf;
    pow /= 2;
  }
  return ans;
}
void fact(int n) {
  long long int fac = 1;
  for (int i = 1; i <= n; i++) {
    fac = ((fac % inf) * (i % inf)) % inf;
    facto[i] = fac;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  facto[0] = 1;
  fact(6000);
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  vector<int> pos;
  for (int i = 0; i < n; i++) {
    if (s[i] == '1') pos.push_back(i);
  }
  if (pos.size() < k) {
    cout << 1 << "\n";
    return 0;
  }
  if (k == 0) {
    cout << 1 << "\n";
    return 0;
  }
  int i = 0, j = k - 1, sz = pos.size();
  long long int ans = 0;
  while (j < sz) {
    if (j != sz - 1) {
      int szz;
      if (i)
        szz = pos[j + 1] - 1 - pos[i - 1];
      else
        szz = pos[j + 1] - 1 - min(pos[i], 0) + 1;
      long long int tot = facto[szz];
      tot = ((tot % inf) * (power(facto[k], inf - 2) % inf)) % inf;
      tot = ((tot % inf) * (power(facto[szz - k], inf - 2) % inf)) % inf;
      szz = pos[j + 1] - 1 - pos[i];
      long long int tot1 = facto[szz];
      tot1 = ((tot1 % inf) * (power(facto[k - 1], inf - 2) % inf)) % inf;
      tot1 = ((tot1 % inf) * (power(facto[szz - k + 1], inf - 2) % inf)) % inf;
      ans = (ans + tot - tot1) % inf;
    } else {
      int szz;
      if (i)
        szz = max(pos[j], n - 1) - pos[i - 1];
      else
        szz = max(pos[j], n - 1) - min(pos[i], 0) + 1;
      long long int tot = facto[szz];
      tot = ((tot % inf) * (power(facto[k], inf - 2) % inf)) % inf;
      tot = ((tot % inf) * (power(facto[szz - k], inf - 2) % inf)) % inf;
      ans = (ans + tot) % inf;
    }
    j += 1;
    i += 1;
  }
  cout << (ans + inf) % inf << "\n";
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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 int inf = 998244353;
long long int facto[1000010];
long long int power(long long int a, long long int pow) {
  long long int ans = 1;
  if (a < 0) a += inf;
  while (pow) {
    if (pow % 2 == 1) {
      ans = ((ans % inf) * (a % inf)) % inf;
    }
    a = ((a % inf) * (a % inf)) % inf;
    if (a < 0) a += inf;
    pow /= 2;
  }
  return ans;
}
void fact(int n) {
  long long int fac = 1;
  for (int i = 1; i <= n; i++) {
    fac = ((fac % inf) * (i % inf)) % inf;
    facto[i] = fac;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  facto[0] = 1;
  fact(6000);
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  vector<int> pos;
  for (int i = 0; i < n; i++) {
    if (s[i] == '1') pos.push_back(i);
  }
  if (pos.size() < k) {
    cout << 1 << "\n";
    return 0;
  }
  if (k == 0) {
    cout << 1 << "\n";
    return 0;
  }
  int i = 0, j = k - 1, sz = pos.size();
  long long int ans = 0;
  while (j < sz) {
    if (j != sz - 1) {
      int szz;
      if (i)
        szz = pos[j + 1] - 1 - pos[i - 1];
      else
        szz = pos[j + 1] - 1 - min(pos[i], 0) + 1;
      long long int tot = facto[szz];
      tot = ((tot % inf) * (power(facto[k], inf - 2) % inf)) % inf;
      tot = ((tot % inf) * (power(facto[szz - k], inf - 2) % inf)) % inf;
      szz = pos[j + 1] - 1 - pos[i];
      long long int tot1 = facto[szz];
      tot1 = ((tot1 % inf) * (power(facto[k - 1], inf - 2) % inf)) % inf;
      tot1 = ((tot1 % inf) * (power(facto[szz - k + 1], inf - 2) % inf)) % inf;
      ans = (ans + tot - tot1) % inf;
    } else {
      int szz;
      if (i)
        szz = max(pos[j], n - 1) - pos[i - 1];
      else
        szz = max(pos[j], n - 1) - min(pos[i], 0) + 1;
      long long int tot = facto[szz];
      tot = ((tot % inf) * (power(facto[k], inf - 2) % inf)) % inf;
      tot = ((tot % inf) * (power(facto[szz - k], inf - 2) % inf)) % inf;
      ans = (ans + tot) % inf;
    }
    j += 1;
    i += 1;
  }
  cout << (ans + inf) % inf << "\n";
  return 0;
}

```