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 _120 {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        int t = 1;
        long [][] table = new long[5001][5001];
        for (int i = 1; i <= 5000; i++) {
            for (int j = 0; j <= i; j++) {
                if (j == 0 || j == i) table[i][j] = 1;
                else {
                    table[i][j] = (table[i - 1][j] + table[i - 1][j - 1]) % mod;
                }
            }
        }
        while (t-- > 0) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            String s = sc.next();
            ArrayList<Integer> a = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (s.charAt(i) == '1') {
                    a.add(i);
                }
            }
            int sz = a.size();
            if (sz < k) {
                out.println(1);
                continue;
            }
            int [] after = new int[n];
            int [] before = new int[n];
            Arrays.fill(after, -1); Arrays.fill(before, -1);
            int cur = 0;
            for (int i = 0; i < n; i++) {
                if (s.charAt(i) == '1') {
                    before[i] = cur;
                    cur = 0;
                } else {
                    ++cur;
                }
            }
            cur = 0;
            for (int i = n - 1; i >= 0; i--) {
                if (s.charAt(i) == '1') {
                    after[i] = cur;
                    cur = 0;
                } else {
                    ++cur;
                }
            }
            int [][] len = new int[sz][sz];
            int [][] ones = new int[sz][sz];
            for (int i = 0; i < sz; i++) {
                for (int j = i; j < sz; j++) {
                    if (i == j) {
                        len[i][j] = before[a.get(i)] + after[a.get(i)] + 1;
                    } else {
                        len[i][j] = a.get(j) - a.get(i) + 1 + before[a.get(i)] + after[a.get(j)];
                    }
                    ones[i][j] = j - i + 1;
                }
            }
            long res = 1;
            for (int l = 1; l <= Math.min(k, sz); l++) {
                for (int i = 0; i <= sz - l; i++) {
                    int j = i + l - 1;
                    if (l == 1) {
                        res = (res + table[len[i][i]][ones[i][i]] - 1) % mod;
                        if (res < 0) res += mod;
                        continue;
                    }
                    res = (res + table[len[i][j]][ones[i][j]]) % mod;
                    res = (res - table[len[i][j - 1]][ones[i][j - 1]]) % mod;
                    if (res < 0) res += mod;
                    res = (res - table[len[i + 1][j]][ones[i + 1][j]]) % mod;
                    if (res < 0) res += mod;
                    if (l == 2) {
                        res = (res + 1) % mod;
                    } else {
                        res = (res + table[len[i + 1][j - 1]][ones[i + 1][j - 1]]) % mod;
                    }
                }
            }
            out.println(res);
        }
        out.close();
    }

    static long mod = (long) 998244353;



    static void sort(int[] a) {
        ArrayList<Integer> q = new ArrayList<>();
        for (int i : a) q.add(i);
        Collections.sort(q);
        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
    }

    static void sort(long[] a) {
        ArrayList<Long> q = new ArrayList<>();
        for (long i : a) q.add(i);
        Collections.sort(q);
        for (int i = 0; i < a.length; i++) a[i] = q.get(i);
    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }


    }

}