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.
5 2
00011
 5 4
11011
 81 5
100000101000000011001101010100001010111000000110000000001000101101111000001000110
 4 3
1011
 47 25
11110011111001110100101010011000110111011011101
 291 159
011001110111110110001111000110001001111100010001011000110100110010001101100110111010101111100111110000110111001100111010001000011001010011011100101000101011010110010011010100100101111010111000001011110101001011101110100100111110011001101010001110110101010101100011101110111000011111011001110
 459 15
101010101010101010101010101010101010101010101111111111111111111111010101010101010101010101011111111111111111111101010101010101010101111111111111111111111101010101010101010111111111111111111111111101010101010101111111111111111111111111110110101010101011111111111111111111111111111001000111111111111111111111111111110000011111111111111111111111111111000001111111111111111111111111111100001111111111111111111111111111100111111111111111111111111111110111111111111
 105 58
110101000111100000011011011101110100001000110011010101100010111001011111010010111101011011010110011011110
 52 11
0110011111001000010000100010010001010100000100110100

10
 5
 187538
 4
 314445058
 1
 0
 132732930
 478323746

import java.io.*;
import java.util.*;

public class d {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer tokenizer = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(tokenizer.nextToken());
        int k = Integer.parseInt(tokenizer.nextToken());
        int mod = 998244353;
        boolean[] input = new boolean[n];
        String s = in.readLine();
        int[] prefix = new int[n];
        int[][] ncr = new int[n + 1][n + 1];
        ncr[0][0] = 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j <= i; j++) {
                ncr[i + 1][j] += ncr[i][j];
                ncr[i + 1][j] %= mod;
                ncr[i + 1][j + 1] += ncr[i][j];
                ncr[i + 1][j + 1] %= mod;
            }
        }
        for (int i = 0; i < ncr.length; i++) {
            // System.out.println(Arrays.toString(ncr[i]));
        }
        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == '1')
                input[i] = true;
            prefix[i] = input[i] ? 1 : 0;
            if (i > 0)
                prefix[i] += prefix[i - 1];
        }
        int answer = 1;
        if (prefix[n - 1] >= k) {
            for (int i = 0; i < n; i++) {
                int pre = i > 0 ? prefix[i - 1] : 0;
                for (int j = i + 1; j < n; j++) {
                    if (prefix[j] > pre + k)
                        continue;
                    int cnt1 = prefix[j] - pre;
                    int cnt0 = j - i + 1 - cnt1;
                    if (input[i]) {
                        cnt0--;
                    } else {
                        cnt1--;
                    }
                    if (input[j]) {
                        cnt0--;
                    } else {
                        cnt1--;
                    }
                    if (cnt0 < 0 || cnt1 < 0)
                        continue;
                    answer += ncr[cnt1 + cnt0][cnt0];
                    answer %= mod;
                }
            }

        }

        System.out.println(answer);
        in.close();
        out.close();
    }
}