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

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

    static class DBicolorings {
        public void solve(int testNumber, FastScanner br, PrintWriter pw) {
            long MOD = 998244353;
            //dp[row][cc][curr]
            int n = br.nextInt();
            int k = br.nextInt();
            long[][][] dp = new long[n][k + 2][4];
            dp[0][1][0] = 1;
            dp[0][2][1] = 1;
            dp[0][2][2] = 1;
            dp[0][1][3] = 1;

            for (int i = 1; i < n; i++) {
                for (int j = 1; j <= k; j++) {
                    for (int mask = 0; mask < 4; mask++) {
                        for (int prev = 0; prev < 4; prev++) {
//                        for(int bit = 0; bit < 2; bit++){
//                            if((mask & (1 << bit)) == (prev & (1 << bit))){
//                                num++;
//                            }
//                        }
                            if (mask == 0 && prev == 0) {
                                dp[i][j][mask] += dp[i - 1][j][prev];
                            } else if (mask == 0 && prev == 1) {
                                dp[i][j][mask] += dp[i - 1][j][prev];
                            } else if (mask == 0 && prev == 2) {
                                dp[i][j][mask] += dp[i - 1][j][prev];
                            } else if (mask == 0 && prev == 3) {
                                dp[i][j][mask] += dp[i - 1][j - 1][prev];
                            } else if (mask == 1 && prev == 0) {
                                dp[i][j][mask] += dp[i - 1][j - 1][prev];
                            } else if (mask == 1 && prev == 1) {
                                dp[i][j][mask] += dp[i - 1][j][prev];
                            } else if (mask == 1 && prev == 2) {
                                if (j > 1) {
                                    dp[i][j][mask] += dp[i - 1][j - 2][prev];
                                }
                            } else if (mask == 1 && prev == 3) {
                                dp[i][j][mask] += dp[i - 1][j - 1][prev];
                            } else if (mask == 2 && prev == 0) {
                                dp[i][j][mask] += dp[i - 1][j - 1][prev];
                            } else if (mask == 2 && prev == 1) {
                                if (j > 1) dp[i][j][mask] += dp[i - 1][j - 2][prev];
                            } else if (mask == 2 && prev == 2) {
                                dp[i][j][mask] += dp[i - 1][j][prev];
                            } else if (mask == 2 && prev == 3) {
                                dp[i][j][mask] += dp[i - 1][j - 1][prev];
                            } else if (mask == 3 && prev == 0) {
                                dp[i][j][mask] += dp[i - 1][j - 1][prev];
                            } else if (mask == 3 && prev == 1) {
                                dp[i][j][mask] += dp[i - 1][j][prev];
                            } else if (mask == 3 && prev == 2) {
                                dp[i][j][mask] += dp[i - 1][j][prev];
                            } else if (mask == 3 && prev == 3) {
                                dp[i][j][mask] += dp[i - 1][j][prev];
                            }
                            dp[i][j][mask] %= MOD;
                        }
//                    pw.println(i + " " + j + " " + Integer.toBinaryString(mask) + " " + dp[i][j][mask]);
                    }
                }
            }
            long ans = 0;
            for (int i = 0; i < 4; i++) {
                ans += dp[n - 1][k][i];
                ans %= MOD;
            }
            pw.println(ans % MOD);
            pw.close();
        }

    }

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

        public FastScanner(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 - '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);

        }

    }
}

