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 new1{
	
	public static long power(long x, long y, int mod) {
	    //System.out.println(x + " ");
		if( y == 0) return 1;
		if( y == 1) return x;
		long a = power(x, y / 2, mod);
		long ans = (a * a) % mod;
		ans = (ans * power(x, y - (y / 2) * 2, mod)) % mod;
		return ans;
	}
	
	public static long modInv(long p, int mod) {
		//System.out.println(p + " " + mod);
		return power(p, mod - 2, mod);
	}
	
	public static long ncr(long[] arr, int n, int r, int mod) {
		long numer = arr[n];
		long denom1 = modInv(arr[r], mod);
		long denom2 = modInv(arr[n - r], mod) ;
		long ans = (numer * denom1) % mod;
		ans = (ans * denom2) % mod;
		return ans;
	}

	public static void main(String[] args)  throws IOException{
    	BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
		FastReader s = new FastReader();
		int n1 = 5004;
		int mod = 998244353;
		long[] arr = new long[n1];
		arr[0] = 1; arr[1] = 1;
		for(int i = 2; i < n1; i++) {
			arr[i] = (arr[i - 1] * i) % mod;
		}
		int t = 1;//s.nextInt();
    	for(int z = 0; z < t; z++) {
    		int n = s.nextInt();
    		int k = s.nextInt();
    		String str = s.next();
    		
    		long ans = 1;
    		for(int i = 0; i < n; i++) {
    			int j = i; int o = 0; int ze = 0;
    			while(j >= 0) {
    				
    				if(str.charAt(j) == '0') ze++;
    				if(str.charAt(j) == '1') o++;
    				if(o > k) {
    					o--;
    					break;
    				}
    				j--;
    			}
    			//
    			//System.out.println(ze + " " + o + " " + i);
    			if(o != k) continue;
    			
    			if(str.charAt(i) == '0') o--;
    			else ze--;
    			
    			if(ze < 0 || o < 0) continue;
    			long aa = ncr(arr, ze + o, ze, mod);
    			ans = (ans + aa) % mod;
    			//System.out.println(ze + " " + o + " " + " " + aa + " " + ans + " " + i);
    			
    			
    		}
    		System.out.println(ans);
    		
    		
    	}
    	//output.flush();

    }
}


class FastReader {
    BufferedReader br;
    StringTokenizer st;
    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    public int nextInt() {
        return Integer.parseInt(next());
    }
 
    long nextLong() {
        return Long.parseLong(next());
    }
 
    double nextDouble() {
        return Double.parseDouble(next());
    }
 
    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
}}