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 E120D {
    static long mod = 998244353;
    static long[][] choose;
    static long[] fact;
	
	public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        
        int n = in.nextInt();
    	int k = in.nextInt();
    	
    	if (k == 0) {
    		out.println(1);
    		out.close();
    		return;
    	}
    	
    	choose = new long[n + 1][n + 1];
    	choose[0][0] = 1;
    	fact = new long[n + 1];
    	fact[0] = 1;
    	
    	String bin = in.nextLine();
    	int[] a = new int[n];
    	for (int i = 0; i < n; i++) a[i] = bin.charAt(i) - '0';
    	int[] pf = new int[n + 1];
    	
    	for (int i = 0; i < n; i++) {
    		pf[i + 1] = pf[i] + a[i];
    	}
    	
    	long ans = 1;
    	
    	if (pf[n] >= k) {
    		for (int i = 0; i < n; i++) {
    			for (int j = i + 1; j < n; j++) {
    				int ct = pf[j + 1] - pf[i];
    				if (ct <= k) {
    					ct -= (a[i] ^ 1) + (a[j] ^ 1);
    					//out.println((j - i - 1) + " " + ct);
    					ans = (ans + nck(j - i - 1, ct)) % mod;
    				}
    			}
    		}
    	}
    	
    	out.println(ans);

        out.close();

    }

	static long nck(int a, int b) {
		if (b < 0 || a < b) return 0;
		if (choose[a][b] != 0) return choose[a][b];
		if (a == b) return choose[a][b] = 1;
		if (b == 0) return choose[a][b] = 1;
		return choose[a][b] = (nck(a - 1, b - 1) + nck(a - 1, b)) % mod;
	}
	
	static long factorial(int a) {
		if (fact[a] != 0) return fact[a];
		return fact[a] = (factorial(a - 1) * a) % mod;
	}

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(InputStream i) {
            br = new BufferedReader(new InputStreamReader(i));
            st = new StringTokenizer("");
        }
        public String next() throws IOException {
            if (st.hasMoreTokens()) {
                return st.nextToken();
            }
            else
                st = new StringTokenizer(br.readLine());
            return next();
        }
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        public String nextLine() throws IOException {
            if (!st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
                return nextLine();
            }

            String ret = "";
            while (st.hasMoreTokens()) {
                ret += st.nextToken();
            }
            return ret;
        }
        public int[] nextIntArr(int size) throws IOException {
            int[] arr = new int[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
        public long[] nextLongArr(int size) throws IOException {
            long[] arr = new long[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }
        public double[] nextDoubleArr(int size) throws IOException {
            double[] arr = new double[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextDouble();
            }
            return arr;
        }
    }
}