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.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public class codeforces_Edu120_D {
    static long mod = 998_244_353;
    static long[] fact = getFact(5000);

    private static long[] getFact(int size) {
        long[] res = new long[size + 1];
        res[0] = 1;
        for (int i = 1; i <= size; i++) {
            res[i] = res[i - 1] * i % mod;
        }
        return res;
    }

    private static long cnk(int n, int k) {
        return fact[n] * pow((fact[k] * fact[n - k] % mod), mod - 2) % mod;
    }

    private static long pow(long a, long b) {
        long res = 1;
        while (b > 0) {
            if (b % 2 == 0) {
                a = (a * a) % mod;
                b /= 2;
            } else {
                res = (res * a) % mod;
                b--;
            }
        }
        return res;
    }

    private static void solve(FastIOAdapter in, PrintWriter out) {
        int n = in.nextInt();
        int k = in.nextInt();
        char[] s = in.next().toCharArray();

        if (k == 0) {
            out.println(1);
            return;
        }
        int st = 0;
        int end = 0;
        int cur = s[0] == '1' ? 1 : 0;
        while (end + 1 < n) {
            if (s[end + 1] == '1') {
                if (cur + 1 <= k) cur++;
                else break;
            }
            end++;
        }

        long ans = 1;
        int prevSt = 1;
        int prevEnd = k;
        while (cur == k && st < n) {
            long cnk = cnk(end - st + 1, k);
            int prevLen = prevEnd - prevSt;
            ans += cnk - 1 - (cnk(prevLen, k - 1) - 1);
            ans %= mod;
            prevSt = st;
            prevEnd = end;
            while (st < n && s[st] == '0') {
                st++;
            }
            st++;
            cur--;
            while (end + 1 < n) {
                if (s[end + 1] == '1') {
                    if (cur + 1 <= k) cur++;
                    else break;
                }
                end++;
            }
        }
        out.println(ans);
    }

    public static void main(String[] args) throws Exception {
        try (FastIOAdapter ioAdapter = new FastIOAdapter()) {
            int count = 1;
            //count = ioAdapter.nextInt();
            while (count-- > 0) {
                solve(ioAdapter, ioAdapter.out);
            }
        }
    }

    static void ruffleSort(int[] arr) {
        int n = arr.length;
        Random rnd = new Random();
        for (int i = 0; i < n; ++i) {
            int tmp = arr[i];
            int randomPos = i + rnd.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = tmp;
        }
        Arrays.sort(arr);
    }

    static class FastIOAdapter implements AutoCloseable {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        public PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter((System.out))));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
                return null;
            }
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readArrayLong(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        @Override
        public void close() throws Exception {
            out.flush();
            out.close();
            br.close();
        }
    }
}
