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.*;
import java.util.concurrent.TimeUnit;

public class d1622 implements Runnable{
    
    public static void main(String[] args) {
        try{
            new Thread(null, new d1622(), "process", 1<<26).start();
        }
        catch(Exception e){
            System.out.println(e);
        }
    }
    public void run() {
        FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
//      try {
//            out = new PrintWriter("file.out");
//        } catch (FileNotFoundException e) {
//            // TODO Auto-generated catch block
//            e.printStackTrace();
//        }
        Task solver = new Task();
//        int t = scan.nextInt();
        int t = 1;
        for(int i = 1; i <= t; i++) solver.solve(i, scan, out);
        out.close();
    }

    static class Task {
        static final int oo = Integer.MAX_VALUE;
        static final long OO = Long.MAX_VALUE;
        static final long MOD = 998244353;

        public void solve(int testNumber, FastReader sc, PrintWriter out) {            
            
            int N = sc.nextInt();
            int K = sc.nextInt();
            String s = sc.nextLine();
            if(K == 0) {
                out.println(1);
                return;
            }
            
            long[] fact = new long[N+1];
            fact[0] = 1;
            for(int i = 1; i < N+1; i++) {
                fact[i] = (fact[i-1] * i) % MOD;
            }
            
            int numOnes = 0;
            long sum = 0;
            boolean flag = false;
            for(int i = 0, j = 0; i < N; i++) {
                if(s.charAt(i) == '1') {
                    numOnes++;
                }
                
                while(numOnes > K) {
                    if(s.charAt(j) == '1') {
                        numOnes--;
                    }
                    j++;
                }
                
                if(numOnes != K) {
                    continue;
                }
                
                int numZeroes = (i - j + 1 - numOnes);
                
                sum += modDivide(fact[i - j + 1], (fact[numZeroes] * fact[numOnes]) % MOD, MOD);
                
                int nZ = numZeroes, nO = numOnes;
                if(s.charAt(i) == '1') {
                    nO--;
                } else {
                    nZ--;
                }
                
                if(flag) {
                    sum -= modDivide(fact[i - j], (fact[nZ] * fact[nO]) % MOD, MOD);
                } else {
                    flag = true;
                }
                
                sum %= MOD;
                while(sum < 0)
                    sum += MOD;
                
//                System.out.println(numOnes + " " + numZeroes);
//                System.out.println(sum);
            }
            
            if(sum == 0)
                out.println(1);
            else
                out.println(sum);
        }
    }
    
    static long modDivide(long a, long b, long MOD) {
        a %= MOD;
        return (binpow(b, MOD-2, MOD) * a) % MOD;
    }
    static long binpow(long a, long b, long m) {
        a %= m;
        long res = 1;
        while (b > 0) {
            if ((b & 1) == 1)
                res = res * a % m;
            a = a * a % m;
            b >>= 1;
        }
        return res;
    }
    static int[] reverse(int a[]) 
    { 
        int[] b = new int[a.length]; 
        for (int i = 0, j = a.length; i < a.length; i++, j--) { 
            b[j - 1] = a[i]; 
        } 
        
        return b;
    }
    static long[] reverse(long a[]) 
    { 
        long[] b = new long[a.length]; 
        for (int i = 0, j = a.length; i < a.length; i++, j--) { 
            b[j - 1] = a[i]; 
        } 
        
        return b;
    }
    static void sort(int[] x){
        shuffle(x);
        Arrays.sort(x);
    }
    static void sort(long[] x){
        shuffle(x);
        Arrays.sort(x);
    }
    static class tup implements Comparable<tup>, Comparator<tup>{
        int a, b;
        tup(int a,int b){
            this.a=a;
            this.b=b;
        }
        public tup() {
        }
        @Override
        public int compareTo(tup o){
            return Integer.compare(b,o.b);
        }
        @Override
        public int compare(tup o1, tup o2) {
            return Integer.compare(o1.b, o2.b);
        }
        
        @Override
        public int hashCode() {
            return Objects.hash(a, b);
        }
 
        @Override
        public boolean equals(Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            tup other = (tup) obj;
            return a==other.a && b==other.b;
        }
        
        @Override
        public String toString() {
            return a + " " + b;
        }
    }
    
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        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;
        }
        
        int[] readArray(int size) {
            int[] a = new int[size];
            for(int i = 0; i < size; i++) {
                a[i] = nextInt();
            }
            return a;
        }
        
        long[] readLongArray(int size) {
            long[] a = new long[size];
            for(int i = 0; i < size; i++) {
                a[i] = nextLong();
            }
            return a;
        }
    }
    
    static void dbg(int[] arr) {
        System.out.println(Arrays.toString(arr));
    }
    static void dbg(long[] arr) {
        System.out.println(Arrays.toString(arr));
    }
    static void dbg(boolean[] arr) {
        System.out.println(Arrays.toString(arr));
    }

    static void dbg(Object... args) {
        for (Object arg : args)
            System.out.print(arg + " ");
        System.out.println();
    }
}