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{
	static FastReader sc=null;
	
	public static void main(String[] args) {
		sc=new FastReader();
		precomp();
		int n=sc.nextInt(),k=sc.nextInt();
		int pre[]=new int[n+1];
		char s[]=sc.next().toCharArray();
		
		int a[]=new int[n];
		for(int i=0;i<n;i++)a[i]=(s[i]-'0');
			
		for(int i=0;i<n;i++)pre[i+1]=pre[i]+a[i];
		
		long ans=1;
		
		if(pre[n]<k) {
			System.out.println(ans);
			return;
		}
		
		for(int i=0;i<n;i++) {
			for(int j=i+1;j<n;j++) {
				//change i and j first and shuffle the between characters
				int ones=pre[j+1]-pre[i];
				if(ones<=k) {
					ones-=(a[i]^1);
					ones-=(a[j]^1);
					
					long ways=NCK(j-i-1,ones);
					ans=add(ans,ways);
				}
			}
		}
		
		System.out.println(ans);
	}
	static long fac[];
	static long invs[];
	
	static int nax=(int)1e4;
	
	static void precomp() {
		fac=new long[nax];
		invs=new long[nax];
		
		fac[0]=1;
		invs[0]=1;
		for(int i=1;i<nax;i++) {
			fac[i]=mul(fac[i-1],i);
			invs[i]=mul(invs[i-1],modInv(i));
		}
	}
	static long NCK(int n,int k) {
		if(n<k || k<0 || n<0)return 0;
		
		return mul(fac[n],mul(invs[k],invs[n-k]));
	}
	
	static long sub(long a,long b) {
		a-=b;
		if(a<0)a+=mod;
		return a;
	}
	static long add(long a,long b) {
		a+=b;
		if(a>=mod)a-=mod;
		return a;
	}
	
	static long mod=(long)998244353;
	
	static long mul(long a ,long b) {
		return (a*b)%mod;
	}

	static long exp(long base,long e) {
		if(e==0) return 1;
		long half=exp(base,e/2);
		if(e%2==0)return mul(half,half);
		return mul(half,mul(half,base));
	}
	
	static long modInv(long a) {
		return exp(a,mod-2);
	}

	
	static int[] ruffleSort(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);
		return a;
	}
	
	static void print(int a[]) {
		for(int e:a) {
			System.out.print(e+" ");
		}
		System.out.println();
	}
	
	static class FastReader{
		
		StringTokenizer st=new StringTokenizer("");
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		String next() {
			while(!st.hasMoreTokens()) 
				try {
					st=new StringTokenizer(br.readLine());
				}
			   catch(IOException e){
				   e.printStackTrace();
			   }
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		int[] readArray(int n) {
			int a[]=new int[n];
			for(int i=0;i<n;i++)a[i]=sc.nextInt();
			return a;
		}
	}
	
	
}
