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 E_Gardener_and_Tree implements Runnable{

       public static void main(String[] args) throws Exception {
        new Thread(null, new E_Gardener_and_Tree(), "E_Gardener_and_Tree", 1<<28).start();
       }
    public void run(){
         WRITE YOUR CODE HERE!!!!
         JUST WRITE EVERYTHING HERE WHICH YOU WRITE IN MAIN!!!
       }

  }
*/
/////**************************************************************************


public class D_Shuffle{
    public static void main(String[] args) {
        FastScanner s= new FastScanner();
        //PrintWriter out=new PrintWriter(System.out);
        //end of program
        //out.println(answer);
        //out.close();
        StringBuilder res = new StringBuilder();
        int n=s.nextInt();
        int k=s.nextInt();
        String str=s.nextToken();
        if(k==0){
            System.out.println("1");
            return;
        }
        long mod=998244353;
        long fact[]= new long[n+5];
        long infact[]= new long[n+5];

        fact[0]=1;
        fact[1]=1;
        for(int i=2;i<n+5;i++){
            fact[i]=(fact[i-1]*i)%mod;
        }
        for(int i=0;i<n+5;i++){
            infact[i]=modpower(fact[i],mod-2,mod);
        }
        long ans=0;
        int flag=0;
        for(int i=0;i<n;i++){
            long count=0;
          //  System.out.println("i "+i);
            int j=i;
              for(;j<n;j++){
                  char ch=str.charAt(j);
                  if(ch=='1'){
                      count++;
                  }
                  if(count>k){
                      break;
                  }
              }
           //   System.out.println("j "+j);

              if(count>=k){
                  flag=1;
                 // String str2=str.substring(i,j);
                  long len=j-i;
                  long ones=k;
                  long zeroes=len-ones;
                  long yoyo1=(fact[(int)len]*infact[(int)ones])%mod;
                  yoyo1=(yoyo1*infact[(int)zeroes])%mod;
                  long yoyo2=0;
                  if(count>k){
                      int l=i;
                      for(;l<n;l++){
                          char ch=str.charAt(l);
                          if(ch=='1'){
                              break;
                          }
                      }
                      l++;
                   //   System.out.println("l "+l);
                      i=l-1;
                      long len1=j-l;
                      long ones1=k-1;
                      long zeroes1=len1-ones1;
                      yoyo2=(fact[(int)len1]*infact[(int)ones1])%mod;
                      yoyo2=(yoyo2*infact[(int)zeroes1])%mod;

                  }
                  else{
                      i=n;
                  }
                  long hh=(yoyo1-yoyo2+mod)%mod;
                  ans=(ans+hh)%mod;
                  ans=(ans+mod)%mod;
              }
              else{
                  break;
              }
            //   System.out.println("kkk "+ans);
            //   System.out.println();

        }
        if(flag==0){
            ans++;
        }
        res.append(ans+" \n");
        System.out.println(res);


    }
    static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
 
		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
 
		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(nextToken());
		}
 
		long nextLong() {
			return Long.parseLong(nextToken());
		}
 
		double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}


    static long modpower(long x, long y, long p)
     {
      long res = 1; // Initialize result
   
      x = x % p; // Update x if it is more than or
      // equal to p
   
      if (x == 0)
        return 0; // In case x is divisible by p;
   
      while (y > 0)
      {
   
        // If y is odd, multiply x with result
        if ((y & 1) != 0)
          res = (res * x) % p;
   
        // y must be even now
        y = y >> 1; // y = y/2
        x = (x * x) % p;
      }
      return res;
    }

  
   // SIMPLE POWER FUNCTION=>


      static long power(long x, long y)
        {
            long res = 1;     // Initialize result
        
            while (y > 0)
            {
            
                // If y is odd, multiply x with result
                if ((y & 1) != 0)
                    res = res * x;
        
                // y must be even now
                y = y >> 1; // y = y/2
                x = x * x;  // Change x to x^2
            }
            return res;
        }





}