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

/*
 * Everything is Hard 
 * Before Easy 
 * Jai Mata Dii 
 */ 
 
import java.util.*;
import java.io.*; 
  
public class Main {
	static class FastReader{ BufferedReader br;StringTokenizer st;public FastReader(){br = new BufferedReader(new InputStreamReader(System.in));}String next(){while (st == null || !st.hasMoreElements()){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());}double nextDouble(){return Double.parseDouble(next());}String nextLine(){String str = ""; try{str = br.readLine(); } catch (IOException e) {e.printStackTrace();} return str; }} 
//	static long mod = (long)(1e9+7); 
	 static long mod = 998244353; 
//	 static Scanner sc = new Scanner(System.in); 
	static FastReader sc = new FastReader(); 
	static PrintWriter out = new PrintWriter(System.out);
	static int ans;
	public static void main (String[] args) {
		int ttt = 1;
//		ttt = sc.nextInt();
		precompute();
		z :for(int tc=1;tc<=ttt;tc++){
			long nx = sc.nextLong();
			long k = sc.nextLong();
			char s[] = sc.next().toCharArray();
			int i = 0, j = 0;
			int cnt = 0, pre = 0;
			long ans = 1;
			boolean isPrev = false;
			while(j<nx) {
				if(s[j] == '1') {
					cnt++;
				}
				if(cnt>k && k!=0) {
//					System.out.println(i+" "+j);
					long n = j - i;
					long r = k;
					
					long cans = ((fac[(int)n] * power(fac[(int)(n-r)],mod-2,mod))%mod * power(fac[(int)r],mod-2,mod))%mod;
					
					ans = (ans + (cans-1L+mod)%mod)%mod;
					
					if(isPrev) {
						n = pre - 1 - i + 1;
						r = k - 1;
						
						cans = ((fac[(int)n] * power(fac[(int)(n-r)],mod-2,mod))%mod * power(fac[(int)r],mod-2,mod))%mod;
						
						ans = (ans - ((cans-1L+mod)%mod) + mod)%mod;
					}
					
					isPrev = true;
					pre = j;
					
					while(i<=j && cnt>k) {
						if(s[i] == '1') cnt--;
						i++;
					}
				}
				j++;
			}
			if(cnt == k && i<=j && k>0) {
//				System.out.println(i+" "+j);
				long n = j - i;
				long r = k;
				
				long cans = ((fac[(int)n] * power(fac[(int)(n-r)],mod-2,mod))%mod * power(fac[(int)r],mod-2,mod))%mod;
				
				ans = (ans + (cans-1L+mod)%mod)%mod;
				
				if(isPrev) {
					n = pre - 1 - i + 1;
					r = k - 1;
					
					cans = ((fac[(int)n] * power(fac[(int)(n-r)],mod-2,mod))%mod * power(fac[(int)r],mod-2,mod))%mod;
					
					ans = (ans - ((cans-1L+mod)%mod) + mod)%mod;
				}
			}
			out.write(ans+"\n");
		}
		out.close();
	}
	
	static long fac[] = new long[100006];
//	static int mod = (int) (1e9+7);
	
	static void precompute() {
		int n = 100005;
		fac[0] = 1;
		for(int i=1;i<=n;i++)
			fac[i] = (i * fac[i-1])%mod;
	}
	
	static int power(long base, long l, long mod2) {
		
		long ans = 1;
		while(l!=0) {
			if(l%2==0) {
				base = (base*base)%mod2;
				l/=2;
			}
			else {
				ans = (ans*base)%mod2;
				l-=1;
			}
		}
		return (int) (ans%mod2);
	}
	
	static long pow(long a, long b){long ret = 1;while(b>0){if(b%2 == 0){a = (a*a)%mod;b /= 2;}else{ret = (ret*a)%mod;b--;}}return ret%mod;}
	static long gcd(long a,long b){if(b==0) return  a; return gcd(b,a%b); } 
	private static void sort(int[] a) {List<Integer> k = new ArrayList<>();for(int val : a) k.add(val);Collections.sort(k);for(int i=0;i<a.length;i++) a[i] = k.get(i);} 
	private static void ini(List<Integer>[] tre2){for(int i=0;i<tre2.length;i++){tre2[i] = new ArrayList<>();}} 
	private static void init(List<int[]>[] tre2){for(int i=0;i<tre2.length;i++){tre2[i] = new ArrayList<>();}} 
	private static void sort(long[] a) {List<Long> k = new ArrayList<>();for(long val : a) k.add(val);Collections.sort(k);for(int i=0;i<a.length;i++) a[i] = k.get(i);} 
}