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.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.FileInputStream;
import java.util.ArrayList;
import java.io.Writer;
import java.io.OutputStreamWriter;
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);
        OutputWriter out = new OutputWriter(outputStream);
        DBicolorings solver = new DBicolorings();
        solver.solve(1, in, out);
        out.close();
    }

    static class DBicolorings {
        private int n;
        private int K;
        private long[][][] dp;

        private long add(long... arr) {
            long res = 0;
            for (int i = 0; i < arr.length; i++) res = res + arr[i];
            return Util.mod(res, 998244353L);
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            n = in.nextInt();
            K = in.nextInt();
            if (K == 1) {
                out.println(2);
                out.flush();
                return;
            }
            if (n == 1) {
                if (K == 2) {
                    out.println(2);
                    out.flush();
                    return;
                } else {
                    out.println(0);
                    out.flush();
                    return;
                }
            }
            dp = new long[n + 1][4][K + 1];
            if (K >= 1) dp[1][0][1] = 1;
            if (K >= 2) dp[1][1][2] = 1;
            if (K >= 2) dp[1][2][2] = 1;
            if (K >= 1) dp[1][3][1] = 1;
            if (K >= 1) dp[2][0][1] = 1;
            if (K >= 2) dp[2][0][2] = 3;
            if (K >= 2) dp[2][1][2] = 3;
            if (K >= 4) dp[2][1][4] = 1;
            if (K >= 2) dp[2][2][2] = 3;
            if (K >= 4) dp[2][2][4] = 1;
            if (K >= 1) dp[2][3][1] = 1;
            if (K >= 2) dp[2][3][2] = 3;
            for (int i = 3; i <= n; i++) {
                for (int k = 1; k <= K; k++) {
                    dp[i][0][k] = add(dp[i - 1][0][k], dp[i - 1][1][k], dp[i - 1][2][k], dp[i - 1][3][k - 1]);
                    if (k - 2 < 0) dp[i][1][k] = add(dp[i - 1][0][k - 1], dp[i - 1][1][k], dp[i - 1][3][k - 1]);
                    else
                        dp[i][1][k] = add(dp[i - 1][0][k - 1], dp[i - 1][1][k], dp[i - 1][2][k - 2], dp[i - 1][3][k - 1]);

                    if (k - 2 < 0) dp[i][2][k] = add(dp[i - 1][0][k - 1], dp[i - 1][2][k], dp[i - 1][3][k - 1]);
                    else
                        dp[i][2][k] = add(dp[i - 1][0][k - 1], dp[i - 1][1][k - 2], dp[i - 1][2][k], dp[i - 1][3][k - 1]);

                    dp[i][3][k] = add(dp[i - 1][0][k - 1], dp[i - 1][1][k], dp[i - 1][2][k], dp[i - 1][3][k]);
                }
            }
            out.println(add(dp[n][0][K], dp[n][1][K], dp[n][2][K], dp[n][3][K]));
            out.flush();
        }

    }

    static class Util {
        public static long mod(long a, long mod) {
            long res = a % mod;
            return res >= 0 ? res : res + mod;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;
        private ArrayList<String> res = new ArrayList<>();
        private StringBuilder sb = new StringBuilder("");

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

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

        public void println(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                sb.append(objects[i]);
            }
            res.add(sb.toString());
            sb = new StringBuilder("");
        }

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

        public void flush() {
            for (String str : res) writer.printf("%s\n", str);
            res.clear();
            sb = new StringBuilder("");
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int numChars;

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

        public InputReader(FileInputStream file) {
            this.stream = file;
        }

        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 = (res << 3) + (res << 1) + c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

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

    }
}

