You are given a grid, consisting of 2 rows and n columns. Each cell of this grid should be colored either black or white.

Two cells are considered neighbours if they have a common border and share the same color. Two cells A and B belong to the same component if they are neighbours, or if there is a neighbour of A that belongs to the same component with B.

Let's call some bicoloring beautiful if it has exactly k components.

Count the number of beautiful bicolorings. The number can be big enough, so print the answer modulo 998244353.

Input

The only line contains two integers n and k (1 ≤ n ≤ 1000, 1 ≤ k ≤ 2n) — the number of columns in a grid and the number of components required.

Output

Print a single integer — the number of beautiful bicolorings modulo 998244353.

Examples

Input

3 4


Output

12


Input

4 1


Output

2


Input

1 2


Output

2

Note

One of possible bicolorings in sample 1:

<image>
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

      static class DBicolorings {
            long[][][] dp;
            long mod = 998244353;

            long rec(int index, int curr, int val, int k, int n) {
                  if (curr > k) {
                        return 0;
                  }
                  if (index == n) {
                        if (curr == k) {
                              return 1;
                        }
                        return 0;
                  }

                  if (dp[index][curr][val] != -1)
                        return dp[index][curr][val];
                  long ans = 0;
                  switch (val) {
                        case 0:
                              ans += rec(index + 1, curr + 1, 2, k, n);
                              ans += rec(index + 1, curr + 1, 1, k, n);
                              ans += rec(index + 1, curr + 1, 3, k, n);
                              ans += rec(index + 1, curr, 0, k, n);
                              break;
                        case 3:
                              ans += rec(index + 1, curr + 1, 1, k, n);
                              ans += rec(index + 1, curr + 1, 2, k, n);
                              ans += rec(index + 1, curr + 1, 0, k, n);
                              ans += rec(index + 1, curr, 3, k, n);
                              break;
                        case 1:
                              ans += rec(index + 1, curr + 2, 2, k, n);
                              ans += rec(index + 1, curr, 1, k, n);
                              ans += rec(index + 1, curr, 0, k, n);
                              ans += rec(index + 1, curr, 3, k, n);
                              break;
                        case 2:
                              ans += rec(index + 1, curr + 2, 1, k, n);
                              ans += rec(index + 1, curr, 2, k, n);
                              ans += rec(index + 1, curr, 0, k, n);
                              ans += rec(index + 1, curr, 3, k, n);
                              break;
                  }
                  dp[index][curr][val] = ans % mod;
                  return ans % mod;
            }

            public void solve(int testNumber, InputReader in, OutputWriter out) {
                  int n = in.nextInt();
                  int k = in.nextInt();
                  dp = new long[n][k + 1][4];
                  for (int i = 0; i < n; i++) {
                        for (int j = 0; j <= k; j++) {
                              Arrays.fill(dp[i][j], -1);
                        }
                  }
                  long ans = rec(1, 1, 0, k, n);
                  ans += rec(1, 2, 1, k, n);
                  ans += rec(1, 2, 2, k, n);
                  ans += rec(1, 1, 3, k, n);
                  out.printLine(ans % mod);

            }

      }

      static class OutputWriter {
            private final PrintWriter writer;

            public OutputWriter(OutputStream outputStream) {
                  writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
            }

            public OutputWriter(Writer writer) {
                  this.writer = new PrintWriter(writer);
            }

            public void close() {
                  writer.close();
            }

            public void printLine(long i) {
                  writer.println(i);
            }

      }

      static class InputReader {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;

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

            public int read() {
                  if (numChars == -1)
                        throw new InputMismatchException();

                  if (curChar >= numChars) {
                        curChar = 0;
                        try {
                              numChars = stream.read(buf);
                        } catch (IOException e) {
                              throw new InputMismatchException();
                        }
                        if (numChars <= 0)
                              return -1;
                  }

                  return buf[curChar++];
            }

            public int nextInt() {
                  int c = read();

                  while (isSpaceChar(c))
                        c = read();

                  int sgn = 1;

                  if (c == '-') {
                        sgn = -1;
                        c = read();
                  }

                  int res = 0;

                  do {
                        if (c < '0' || c > '9')
                              throw new InputMismatchException();

                        res *= 10;
                        res += c & 15;

                        c = read();
                  } while (!isSpaceChar(c));

                  return res * sgn;
            }

            public boolean isSpaceChar(int c) {
                  return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }

      }
}

