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

public class D {

    static FastScanner fs = new FastScanner();
    static Scanner scn = new Scanner(System.in);
    static PrintWriter pw = new PrintWriter(System.out);
    static StringBuilder sb = new StringBuilder("");
    final static long MOD = 998244353;
    final static int INF = 1000000000;

    public static void main(String[] args) {
        int n = fs.nextInt(), k = fs.nextInt();
        String s = fs.next();
        int[][] binom = new int[n+1][n+1];
        for (int i = 0; i <= n; i++) {
            binom[i][0] = 1;
            for (int j = 1; j < i; j++) {
                binom[i][j] = binom[i-1][j-1] + binom[i-1][j];
                if (binom[i][j] >= MOD) binom[i][j] -= MOD;
            }
            binom[i][i] = 1;
        }
        int cnt = 0;
        for (int i = 0; i < n; i++) if (s.charAt(i) == '1') cnt++;
        if (cnt < k) sb.append("1\n");
        else {
            long ans = 0;
            for (int i = 0; i < n; i++) {
                int cnt0 = 0, cnt1 = 0;
                for (int j = i; j < n; j++) {
                    if (cnt1 == k && s.charAt(j) == '1') break;
                    if (s.charAt(j) == '0') cnt0++;
                    if (s.charAt(j) == '1') cnt1++;
                }
                if (s.charAt(i) == '0' && cnt1 >= 1) ans += binom[cnt0 + cnt1 - 1][cnt0];
                if (s.charAt(i) == '1' && cnt0 >= 1) ans += binom[cnt0 + cnt1 - 1][cnt1];
            }
            ans++;
            ans %= MOD;
            sb.append(ans + "\n");
        }
        pw.print(sb.toString());
        pw.close();
    }
    
    static void sort(int[] a) {
        ArrayList<Integer> al = new ArrayList<>();
        for (int i : a)
            al.add(i);
        Collections.sort(al);
        for (int i = 0; i < a.length; i++)
            a[i] = al.get(i);
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {while (!st.hasMoreTokens()) try {st = new StringTokenizer(br.readLine());} catch (IOException e) {}return st.nextToken();}
        int nextInt() {return Integer.parseInt(next());}
        long nextLong() {return Long.parseLong(next());}
        double nextDouble() {return Double.parseDouble(next());}
    }
}