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.Scanner;

public class Main {
    
    static final long MOD = 998244353;

    public static void main(String[] args) {
    
        var sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        int k = Integer.parseInt(sc.next());
        String s = sc.next();
        
        if(k == 0){
            System.out.println(1);
            return;
        }else if(k == 1){
            long ans = 1;
            for(int i = 0; i < n; i++){
                if(s.charAt(i) == '0') continue;
                int l = i;
                int r = i;
                while(0 < l && s.charAt(l-1) == '0'){
                    l--;
                }
                while(r < n-1 && s.charAt(r+1) == '0'){
                    r++;
                }
                ans += r-l;
            }
            System.out.println(ans);
            return;
        }
        
        long ans = 0;
        int l = 0;
        int r = 0;
        int count = s.charAt(0) == '0' ? 0 : 1;
        while(true){
            int r2 = 0;
            while(r < n-1 && (count < k || s.charAt(r+1) == '0')){
                r++;
                if(s.charAt(r) == '1'){
                    count++;
                    r2 = r;
                }
            }
            if(count < k) break;
            
            if(l == 0){
                ans += combination(r-l+1, count);
            }else{
                if(r-l+1 > count){
                    ans += combination(r-l+1, count);
                    if(r2-l+1 >= count){
                        ans -= combination(r2-l+1, count);
                    }
                    if(r2-l >= count){
                        ans += combination(r2-l, count);
                    }
                }
            }
            
            if(r == n-1) break;
            while(l < r && count == k){
                if(s.charAt(l) == '1'){
                    count--;
                }
                l++;
            }
        }
        if(ans == 0) ans = 1;
        System.out.println(ans);
    }
    
    static long combination(long n, long r){
        if(n-r < r) r = n-r;
        long x = 1;
        long y = 1;
        for(int i = 0; i < r; i++){
            x *= n-i;
            x %= MOD;
            y *= i+1;
            y %= MOD;
        }
        x *= modinv(y);
        x %= MOD;
        return x;
    }
    
    static long modinv(long a){
        long b = MOD;
        long u = 1;
        long v = 0;
        long t, tmp;
        while(b != 0){
            t = a/b;
            a -= t*b;
            tmp = a;
            a = b;
            b = tmp;
            u -= t*v;
            tmp = u;
            u = v;
            v = tmp;
        }
        u %= MOD;
        if(u < 0) u += MOD;
        return u;
    }
}