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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author dauom
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    DShuffle solver = new DShuffle();
    solver.solve(1, in, out);
    out.close();
  }

  static class DShuffle {
    private static final ModArithmetic mod = new ModArithmetic(998244353, true);
    private static final int[][] fif = mod.getFactorialAndInverse(5005);
    private static final int[] f = fif[0];
    private static final int[] fi = fif[1];

    private static int ways(int z, int o) {
      return mod.mul(f[o + z], fi[o], fi[z]);
    }

    public final void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();
      int k = in.nextInt();
      char[] s = in.nextCharArray();
      if (k == 0) {
        out.println("1");
        return;
      }

      int ans = 1;
      int l = 0, r = -1;
      int c = 0;
      while (l < n) {
        while (c <= k && r + 1 < n) {
          c += s[++r] - '0';
        }
        if (c < k) break;

        int total = r - l + (c == k ? 1 : 0);
        int ones = c - (c == k ? 0 : 1);
        int zeroes = total - ones;
        ans = mod.add(ans, mod.sub(ways(zeroes, ones), 1));
//      out.println(l + "," +  r + " : " + zeroes + " " + ones);
//      out.println("+" + mod.sub(ways(zeroes, ones), 1));
        if (r == n - 1) break;

        if (s[l] == '0') --zeroes;
        else --ones;
        ans = mod.sub(ans, mod.sub(ways(zeroes, ones), 1));
//      out.println("-" + mod.sub(ways(zeroes, ones), 1));
        while (c > k && l <= r) {
          c -= s[l++] - '0';
        }
      }
      out.println(ans);
    }

  }

  static final class InputReader {
    private final InputStream stream;
    private final byte[] buf = new byte[1 << 18];
    private int curChar;
    private int numChars;

    public InputReader() {
      this.stream = System.in;
    }

    public InputReader(final InputStream stream) {
      this.stream = stream;
    }

    private int read() {
      if (this.numChars == -1) {
        throw new UnknownError();
      } else {
        if (this.curChar >= this.numChars) {
          this.curChar = 0;

          try {
            this.numChars = this.stream.read(this.buf);
          } catch (IOException ex) {
            throw new InputMismatchException();
          }

          if (this.numChars <= 0) {
            return -1;
          }
        }

        return this.buf[this.curChar++];
      }
    }

    public final int nextInt() {
      int c;
      for (c = this.read(); isSpaceChar(c); c = this.read()) {
      }

      byte sgn = 1;
      if (c == 45) { // 45 == '-'
        sgn = -1;
        c = this.read();
      }

      int res = 0;

      while (c >= 48 && c <= 57) { // 48 == '0', 57 == '9'
        res *= 10;
        res += c - 48; // 48 == '0'
        c = this.read();
        if (isSpaceChar(c)) {
          return res * sgn;
        }
      }

      throw new InputMismatchException();
    }

    public final String next() {
      int c;
      while (isSpaceChar(c = this.read())) {
      }

      StringBuilder result = new StringBuilder();
      result.appendCodePoint(c);

      while (!isSpaceChar(c = this.read())) {
        result.appendCodePoint(c);
      }

      return result.toString();
    }

    private static boolean isSpaceChar(final int c) {
      return c == 32 || c == 10 || c == 13 || c == 9
          || c == -1; // 32 == ' ', 10 == '\n', 13 == '\r', 9 == '\t'
    }

    public final char[] nextCharArray() {
      return next().toCharArray();
    }

  }

  static final class ModArithmetic {
    public static final int DEFAULT_MOD = 1_000_000_007;
    public final int m;
    public final boolean isPrime;

    public ModArithmetic() {
      this(DEFAULT_MOD, true);
    }

    public ModArithmetic(int mod) {
      this(mod, false);
    }

    public ModArithmetic(int mod, boolean isPrime) {
      if (mod <= 0) {
        throw new IllegalArgumentException("Modulo must be > 0");
      }
      this.m = mod;
      this.isPrime = isPrime;
    }

    public final int add(int a, int b) {
      a += b;
      if (a >= m) {
        a -= m;
      }
      return a;
    }

    public final int sub(int a, int b) {
      a -= b;
      if (a < 0) {
        a += m;
      }
      return a;
    }

    public final int mul(int a, int b) {
      long m = a * (long) b;
      if (m >= this.m) {
        m %= this.m;
      }
      return (int) m;
    }

    public final int mul(int a, int b, int... c) {
      long m = a * (long) b;
      if (m >= this.m) {
        m %= this.m;
      }
      for (int x : c) {
        m *= x;
        if (m >= this.m) {
          m %= this.m;
        }
      }
      return (int) m;
    }

    public final int div(int a, int b) {
      if (isPrime) {
        return mul(a, pow(b, m - 2));
      }
      throw new UnsupportedOperationException();
    }

    public final int pow(long a, long b) {
      long res = 1;
      while (b > 0) {
        if ((b & 1) == 1) {
          res *= a;
          if (res >= m) {
            res %= m;
          }
        }
        b >>= 1;
        a *= a;
        if (a >= m) {
          a %= m;
        }
      }
      return (int) res;
    }

    public final int[][] getFactorialAndInverse(int n) {
      int[] f = new int[n + 1];
      int[] fi = new int[n + 1];
      f[0] = 1;
      for (int i = 1; i <= n; i++) {
        f[i] = mul(f[i - 1], i);
      }
      fi[n] = div(1, f[n]);
      for (int i = n - 1; i >= 0; i--) {
        fi[i] = mul(fi[i + 1], i + 1);
      }
      return new int[][]{f, fi};
    }

    public String toString() {
      return "ModArithmetic{" + "m=" + m + ", isPrime=" + isPrime + '}';
    }

  }
}

