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.*;

public class Main {
    // For fast input output
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            try {
                br = new BufferedReader(
                        new FileReader("input.txt"));
                PrintStream out = new PrintStream(new FileOutputStream("output.txt"));
                System.setOut(out);
            } catch (Exception e) {
                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;
        }
    }

    // end of fast i/o code
    public static void main(String[] args) {
        FastReader reader = new FastReader();
        

        int n = reader.nextInt();
        int k = reader.nextInt();
        long mod = 998244353;        

        String s = reader.nextLine();
        long factorial[] = new long[5001];
        long prev = 1;
        factorial[0] = 1;
        for(int i=1; i<=5000; i++){
            factorial[i] = (i*prev)%mod;
            prev = factorial[i];
        }

        int curr_len = 0;
        boolean last = false;

        int start = 0;
        int ones = 0;
        long ans = 0;
        long current;
        int end = 0;

        if(k==0){
            System.out.println("1");
            return;
        }

        for(end = 0; end<n; end++){
            if(s.charAt(end)=='1'){
                ones++;
            }
            if(ones > k){

                // adding something in ans
                current = (factorial[end-start] * fast_pow(factorial[k], mod-2, mod))%mod;
                current = (current * fast_pow(factorial[end-start - k], mod-2, mod))%mod;
                // System.out.println(current + "<-> "+start+" "+end+" "+factorial[end-start]);
                ans = (ans + current)%mod;
                
                while(start < n && ones > k){
                    if(s.charAt(start)=='1'){
                        start++;
                        ones--;
                        break;
                    }
                    start++;
                }

                current = (factorial[end-start] * fast_pow(factorial[ones-1], mod-2, mod))%mod;
                current = (current * fast_pow(factorial[end-start - (ones-1)], mod-2, mod))%mod;
                // System.out.println(current + "<- "+start+" "+end);
                ans = (ans - current)%mod;

                // System.out.println(ans+"<->");
            }
        }
        if(ones==k){
            current = (factorial[end-start] * fast_pow(factorial[ones], mod-2, mod))%mod;
            current = (current * fast_pow(factorial[end-start - ones], mod-2, mod))%mod;
            // System.out.println(current + "<-> "+start+" "+end+" "+factorial[end-start]+" "+ones+" "+(end-start - ones));
            // System.out.println(fast_pow(1L*ones, mod-2, mod)+" ;;");
            // System.out.println(fast_pow(1L*(end-start - ones), mod-2, mod)+" ;;");
            ans = (ans + current)%mod;
        }

        if(ans==0){
            ans = 1;
        }
        System.out.println(ans);
    }

    static long fast_pow(long a, long b, long mod){
        if(b==0){
            return 1L;
        }
        // if(b==1){
        //     return a;
        // }
        if(b%2==1){
            return (a * fast_pow(a, b-1, mod))%mod;
        }else{
            return fast_pow((a*a)%mod, b/2, mod);
        }
    }
}