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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class d {
	public static void main(String[] args) {
		FastScanner scan=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);

		int n=scan.nextInt();
		int k=scan.nextInt();
		char[] aa=scan.next().toCharArray();
		int[] a=new int[n];
		int ones=0;
		for(int i=0;i<n;i++) {
			a[i]=(int)(aa[i]-'0');
			if(a[i]==1) ones++;
		}
		
		if(k==0||k>ones) {
			out.println(1);
		}
		else {
			fac=new long[n+1];
			invfac=new long[n+1];
			fac[0]=invfac[0]=1;
			
			for(int i=1;i<fac.length;i++) {
				fac[i]=mult(fac[i-1],i);
				invfac[i]=pow(fac[i],MOD-2);
			}
			long res=0L;
			int l=0, r=0;
			int f=0;
			while(l<n) {
				int end=-1;
				while(r<n&&f<=k) {
					if(f==k&&end==-1) end=r;
					if(a[r]==1&&f+1>k) break;
					else if(a[r]==1) f++;
					r++;
				}
				if(k!=f) break;
//				System.out.println(l+" "+r);
				int leftspace=end-l;
				int rightspace=r-end;
				if(l==0) {
					res=add(res,choose(leftspace+rightspace,k));
				}
				else if(r==n) {
					res=add(res,choose(leftspace+rightspace-1,k));
				}
				else {
//					System.out.println("left "+leftspace+" right "+rightspace);
					res=add(res,choose(leftspace+rightspace-1,k));
					res=add(res,choose(rightspace+1,k-1));
				}
				while(f==k) {
					if(a[l++]==1) f--;
				}
			}
			out.println(res);
		}
		out.close();
	}
	public static long pow(long b, long e) {
		if(e==0L) return 1L;
		if(e%2==0) {
			long temp=pow(b,e/2);
			return mult(temp,temp);
		}
		return mult(b,pow(b,e-1));
	}
	static long[] fac,invfac;
	static long choose(int n, int k) {
		if(n<k) return 0;
		return fac[n]*invfac[n-k]*invfac[k];
	}
	public static long add(long a, long b) {
		return (a%MOD+b%MOD)%MOD;
	}
	public static long mult(long a, long b) {
		return ((a%MOD)*(b%MOD))%MOD;
	}
	static final int MOD=998244353;
	static long[][][] dp;
	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			try	{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e){e.printStackTrace();}
		}

		public String next() {
			if (st.hasMoreTokens())	return st.nextToken();
			try {st = new StringTokenizer(br.readLine());}
			catch (Exception e) {e.printStackTrace();}
			return st.nextToken();
		}

		public int nextInt() {return Integer.parseInt(next());}

		public long nextLong() {return Long.parseLong(next());}

		public double nextDouble() {return Double.parseDouble(next());}

		public String nextLine() {
			String line = "";
			if(st.hasMoreTokens()) line = st.nextToken();
			else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
			while(st.hasMoreTokens()) line += " "+st.nextToken();
			return line;
		}
	}
}
