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 _1622_D {
    static long MOD = 998244353;
    static long[] fact = new long[5005];
    static long[] inv_fact = new long[5005];
    public static void main(String[] args) throws IOException {
        long cur1 = 1;
        long cur2 = 1;
        for(int i = 1; i < 5005; i++) {
            cur1 = modmult(cur1, i);
            cur2 = modmult(cur2, modinv(i));
            fact[i] = cur1;
            inv_fact[i] = cur2;
        }
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringTokenizer line = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(line.nextToken());
        int k = Integer.parseInt(line.nextToken());
        String s = in.readLine();
        int total = 0;
        for(int i = 0; i < n; i++) {
            if(s.charAt(i) == '1') {
                total++;
            }
        }
        long res = 0;
        int sign = 1;
        for(int i = k; i >= 1; i--) {
            res = modadd(res, sign * calc(n, k, s, i, total));
            sign *= -1;
        }
        if(k == 1) {
            res -= (total - 1);
        }
        out.println(Math.max(1, res));
        in.close();
        out.close();
    }  
    static long calc(int n, int k, String s, int w, int total) {
        long res = 0;
        int r = 0;
        int count = 0;
        int ones = 0;
        for(int i = 0; i < n; i++) {
            if(i == 0 || s.charAt(i - 1) == '1') {
                if(i > 0) {
                    count--;
                    ones++;
                }
                while(r < n) {
                    if(s.charAt(r) == '1') {
                        count++;
                        if(count > w) {
                            count--;
                            break;
                        }
                    }
                    r++;
                }
                if(ones >= k - w && count == w && total - (ones + w) >= k - w) {
                    res = modadd(res, binom(r - i, w));
                }
            }
        }
        return res;
    }
    static long binom(int n, int k) {
        return modmult(modmult(fact[n], inv_fact[n - k]), inv_fact[k]);
    }
    static long modadd(long a, long b) {
        return (a + b + MOD) % MOD;
    }
    static long modmult(long a, long b) {
        return a * b % MOD;
    }
    static long modinv(long a) {
        return binpow(a, MOD - 2);
    }
    static long binpow(long a, long b) {
        if(b == 0) {
            return 1;
        }
        long small = binpow(a, b / 2);
        if(b % 2 == 0) {
            return modmult(small, small);
        }else {
            return modmult(modmult(small, small), a);
        }
    }
}
