description: 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.
solution: import java.io.*;
  import java.util.*;
  
  public class D {
  
  	static long MOD = 998244353;
  	static long[] factorial = new long[50001];
  	
  	public static void main(String[] args) throws IOException {
  
  		factorial[0] = 1;
  		
  		for (long i = 1; i <= 5000; i++)
  		    factorial[(int) i] = factorial[(int) (i - 1)] * i % MOD;
  		
  		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  		PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
  		StringTokenizer st = new StringTokenizer(br.readLine());
  		
  		int n = Integer.parseInt(st.nextToken());
  		int k = Integer.parseInt(st.nextToken());
  		
  		char[] ar = br.readLine().toCharArray();
  		
  		int l = -1;
  		int r = -1;		
  		int foc = 0;
  		int roc = 0;
  		int cnt = 0;
  		boolean first = true;
  		
  		long tot = 0;
  		
  		for(int i = 0; i < n; i++) {
  			
  			if(ar[i] == '1') {
  				
  				if(cnt == k && l != -1) {
  					
  					foc = roc = 0;
  					
  					for(int j = r-1; j >= 0; j--) {
  						
  						if(ar[j] == '1' && j < l)
  							break;
  						
  						if(ar[j] == '0')
  							foc++;
  						
  					}
  					
  					for(int j = r+1; j < n; j++) {
  						
  						if(ar[j] == '1')
  							break;
  						
  						roc++;
  						
  					}
  					
  					long add = bincoef(k+foc+roc, k) - ((first) ? 1 : bincoef(k+foc-1, k-1));
  							
  					if(add < 0)
  						add += MOD;
  							
  					tot = (tot + add) % MOD;
  					
  					first = false;
  															
  					//System.out.println(l + " " + r + " " + foc + " " + roc + " " + tot);
  											
  				}
  				
  				if(l == -1) {
  					
  					l = i;
  					r = i;
  					
  				}else
  					r = i;
  				
  				cnt++;
  				
  				if(cnt > k) {
  					
  					for(int j = l+1; j <= r; j++) {
  						
  						if(ar[j] == '1') {
  							
  							l = j;
  							break;
  							
  						}
  						
  					}
  					
  					cnt--;
  					
  				}
  												
  			}
  			
  		}
  		
  		if(cnt == k) {
  			
  			foc = roc = 0;
  			
  			for(int j = r-1; j >= 0; j--) {
  				
  				if(ar[j] == '1' && j < l)
  					break;
  				
  				if(ar[j] == '0')
  					foc++;
  				
  			}
  			
  			for(int j = r+1; j < n; j++) {
  				
  				if(ar[j] == '1')
  					break;
  				
  				roc++;
  				
  			}
  									
  			long add = bincoef(k+foc+roc, k) - ((first) ? 1 : bincoef(k+foc-1, k-1));
  			
  			if(add < 0)
  				add += MOD;
  					
  			tot = (tot + add) % MOD;
  			
  			//System.out.println(l + " " + r + " " + foc + " " + roc + " " + tot);
  									
  		}
  		
  		System.out.println((tot+1)%MOD);
  
  	}
  	
  	static long bincoef(int n, int k) {
  		
  		if(n <= 0)
  			return 1;
  		
  		if(k <= 0)
  			return 1;
  		
  	    return factorial[n] * binpow(factorial[k] * factorial[n - k] % MOD, MOD - 2) % MOD;
  	    
  	}
  	
  	static long binpow(long a, long b) {
  		
  	    a %= MOD;
  	    
  	    long res = 1;
  	    
  	    while (b > 0) {
  	    	
  	        if ((b & 1) == 1)
  	            res = res * a % MOD;
  	        
  	        a = a * a % MOD;
  	        b >>= 1;
  	        
  	    }
  	    
  	    return res;
  	    
  	}
  
  }
  