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.*;
import java.lang.reflect.Array;

public class Main {
	public static final int N = 5005, mod = 998244353;
	public static int n, k;
	public static char[] s = new char[N];
	public static int Pow(long a, long b) {
		long ans = 1;
		while(b != 0) {
			if((b & 1) != 0) ans = ans * a % mod;
			a = a * a % mod;
			b >>= 1;
		}
		return (int) (ans % mod);
	}
	public static int[] fac = new int[N], ifac = new int[N];
	public static void init(int n) {
		fac[0] = 1;
		for(int i = 1; i<=n; i++) fac[i] = (int) (((long)fac[i-1] * i) % mod);
		ifac[n] = Pow(fac[n], mod-2);
		for(int i=n-1; i>=0; i--) ifac[i] = (int) ((long) ifac[i+1]*(i+1)%mod);
	}
	public static int C(int a, int b) {
		if(a<b||b<0) return 0;
		return (int) (((long)fac[a])*ifac[b]%mod*ifac[a-b]%mod);
	}
	public static void main(String[] args) throws IOException {
		//scanf("%d%d%s", &n, &k, s+1);
		BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(input.readLine());
		n = Integer.parseInt(st.nextToken());
		k = Integer.parseInt(st.nextToken());
		
		String tttemp = input.readLine();
		for(int i = 1;i<=n;i++) {
			s[i] = tttemp.charAt(i - 1);
		}
		
		if(k == 0) {
			System.out.println(1);
			return;
		}
		init(n);
		int cnt = 0, ans = 0;
		for(int i=1, j=1; i<=n; i++) {
			if(s[i]=='0') continue;
			++cnt;
			if(cnt<k) continue;
			boolean f = false;
			while(cnt>k) {
				f = true;
				cnt -= s[j] - '0';
				++j;
			}
			if(f) ans = (ans - C(i-j, k-1) + mod)%mod;
			++i;
			while(i<=n && s[i]=='0') ++i;
			--i;
			ans = (ans + C(i-j+1, k))%mod;
		}
		if(cnt<k) ans = 1;
		System.out.println(ans);
}
}
