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.*;
import java.util.*;

public class CF1622D extends PrintWriter {
	CF1622D() { super(System.out, true); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1622D o = new CF1622D(); o.main(); o.flush();
	}

	static final int MD = 998244353;
	void main() {
		int n = sc.nextInt();
		int k = sc.nextInt();
		int[][] ch = new int[n + 1][k + 1];
		ch[0][0] = 1;
		for (int a = 1; a <= n; a++) {
			ch[a][0] = 1;
			for (int b = 1; b <= k; b++) 
				ch[a][b] = (ch[a - 1][b] + ch[a - 1][b - 1]) % MD;
		}
		byte[] cc = sc.next().getBytes();
		int[] qu = new int[n + 2];
		int cnt = 0;
		qu[cnt++] = 0;
		for (int i = 1; i <= n; i++)
			if (cc[i - 1] == '1')
				qu[cnt++] = i;
		qu[cnt++] = n + 1;
		if (cnt - 2 < k || k == 0) {
			println(1);
			return;
		}
		long ans = 1;
		for (int i = 1; i + k < cnt; i++) {
			int a = qu[i + k] - qu[i - 1] - 1;
			int b = qu[i + k] - qu[i] - 1;
			ans += ch[a][k];
			ans -= ch[b][k - 1];
		}
		for (int h = 1; h < k; h++) {
			int a = qu[cnt - 1] - qu[cnt - 1 - h - 1] - 1;
			int b = qu[cnt - 1] - qu[cnt - 1 - h] - 1;
			ans += ch[a][h];
			ans -= ch[b][h - 1];
		}
		ans %= MD;
		if (ans < 0)
			ans += MD;
		println(ans);
	}
}
