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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        long mod = 998244353L;
        long[][][][] dp;
        int n = 0;
        int k = 0;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.ni();
            k = in.ni();
            dp = new long[n + 2][2 * n + 2][2][2];
            long ans;
            for (int i = 0; i <= n + 1; ++i) {
                for (int j = 0; j <= 2 * n + 1; ++j) {
                    for (int k = 0; k < 2; ++k) {
                        for (int l = 0; l < 2; ++l) dp[i][j][k][l] = -1;
                    }
                }
            }
            ans = (solv(2, 1, 1, 1) + solv(2, 1, 0, 0)) % mod;
            ans = (ans + solv(2, 2, 0, 1) + solv(2, 2, 1, 0)) % mod;
            System.out.print(ans);
        }

        public long solv(int pos, int fill, int u, int d) {
            if (fill > k) return 0;
            if (pos == n + 1) {
                if (fill == k) return 1;
                else return 0;
            }
            if (dp[pos][fill][u][d] != -1) return dp[pos][fill][u][d];
            long ans = 0;
            if (u == d) {
                ans += solv(pos + 1, fill, u, d);
                ans += solv(pos + 1, fill + 1, u ^ 1, d ^ 1);
                ans += solv(pos + 1, fill + 1, u ^ 1, d);
                ans += solv(pos + 1, fill + 1, u, d ^ 1);
            } else {
                ans += solv(pos + 1, fill, u, d);
                ans += solv(pos + 1, fill, 1, 1);
                ans += solv(pos + 1, fill, 0, 0);
                ans += solv(pos + 1, fill + 2, u ^ 1, d ^ 1);
            }
            ans %= mod;
            dp[pos][fill][u][d] = ans;
            return ans;
        }

    }

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

        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 ni() {
            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 - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

