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.*;

public class D {
    static long[] fact, inv;
    static int n, k;
    static int[] arr;
    static long MOD = (long)998244353;
    public static void main(String[] args) throws IOException{
        FastIO file = new FastIO();
        n = file.nextInt();
        k = file.nextInt();
        String s = file.next();
        int[] ones = new int[n];
        int cnt = 0;
        arr = new int[n];
        for (int i=0; i<n; i++){
            arr[i] = s.charAt(i)-'0';
            if (arr[i] == 1){
                ones[cnt++] = i;
            }
        }
        setupCombination(n);
        if (cnt < k || k == 0){
            file.println(1);
        }else if (cnt == k){
            file.println(C(n, k));
        }else{
            long ans = 0;
            for (int i=k-1; i<cnt; i++){
                int l = 0;
                if (i-k >= 0){
                    l = ones[i-k]+1;
                }
                int r = n-1;
                if (i+1 < cnt){
                    r = ones[i+1]-1;
                }
                if (r-l+1 < k){
                    System.out.println();
                }
                ans = add(ans, C(r-l+1, k));
                if (i != k-1){
                    ans = subtract(ans, C(ones[i]-l, k-1));
                }
            }
            file.println(ans);
        }
        file.close();
    }
    public static void setupCombination(int n){
        fact = new long[n+1]; // factorial
        inv = new long[n+1]; // inv[i] = multiplicative inverse of i factorial
        fact[0] = 1;
        inv[0] = 1;
        for (int i=1; i<=n; i++){
            fact[i] = multiply(fact[i-1], i);
            inv[i] = multiply(inv[i-1], binpow(i, MOD-2));
        }
    }
    public static long C(int a, int b){ // a choose b
        return multiply(fact[a], multiply(inv[b], inv[a-b]));
    }
    public static long subtract(long a, long b){
        return (((a%MOD) - (b%MOD)) + MOD)%MOD;
    }
    public static long binpow(long a, long b){ // Iterative binary exponentiation
        long res = 1;
        while (b > 0){
            if (b % 2 != 0){
                res = multiply(a, res);
            }
            a = multiply(a, a);
            b /= 2;
        }
        return res; 
    }
    public static long multiply(long a, long b){
        return ((a%MOD) * (b%MOD))%MOD;
    }
    public static long add(long a, long b){
        return ((a%MOD) + (b%MOD))%MOD;
    }
    static class FastIO extends PrintWriter {
        private InputStream stream;
        private byte[] buf = new byte[1<<16];
        private int curChar, numChars;
    
        public FastIO() { this(System.in,System.out); }
        public FastIO(InputStream i, OutputStream o) {
            super(o);
            stream = i;
        }
        public FastIO(String i, String o) throws IOException {
            super(new FileWriter(o));
            stream = new FileInputStream(i);
        }
        public FastIO(String i) throws IOException {
            super(System.out);
            stream = new FileInputStream(i);
        }
        // throws InputMismatchException() if previously detected end of file
        private int nextByte() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars == -1) return -1; // end of file
            }
            return buf[curChar++];
        }
        // to read in entire lines, replace c <= ' '
        // with a function that checks whether c is a line break
        public String next() {
            int c; do { c = nextByte(); } while (c <= ' ');
            StringBuilder res = new StringBuilder();
            do { res.appendCodePoint(c); c = nextByte(); } while (c > ' ');
            return res.toString();
        }
        public int nextInt() {
            int c; do { c = nextByte(); } while (c <= ' ');
            int sgn = 1; if (c == '-') { sgn = -1; c = nextByte(); }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = 10*res+c-'0';
                c = nextByte();
            } while (c > ' ');
            return res * sgn;
        }
        public long nextLong() {
            int c; do { c = nextByte(); } while (c <= ' ');
            int sgn = 1; if (c == '-') { sgn = -1; c = nextByte(); }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = 10*res+c-'0';
                c = nextByte();
            } while (c > ' ');
            return res * sgn;
        }
        public double nextDouble() { return Double.parseDouble(next()); }
    }
}