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
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public static final long MODULO = 998244353;

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int K = in.nextInt();

            long[][][] dp = new long[n][K][4];
            dp[0][0][0] = 1;
            dp[0][0][3] = 1;

            if (K > 1) {
                dp[0][1][1] = 1;
                dp[0][1][2] = 1;
            }

            for (int i = 1; i < n; ++i) {
                for (int j = 0; j < K; ++j) {
                    for (int l = 0; l < 4; ++l) {
                        if (l == 0 || l == 3) {
                            dp[i][j][l] = add(dp[i][j][l], dp[i - 1][j][l]);
                            if (j + 1 < K) {
                                dp[i][j + 1][l ^ 1] = add(dp[i][j + 1][l ^ 1], dp[i - 1][j][l]);
                                dp[i][j + 1][l ^ 2] = add(dp[i][j + 1][l ^ 2], dp[i - 1][j][l]);
                                dp[i][j + 1][l ^ 3] = add(dp[i][j + 1][l ^ 3], dp[i - 1][j][l]);
                            }
                        } else {
                            dp[i][j][l] = add(dp[i][j][l], dp[i - 1][j][l]);
                            dp[i][j][l ^ 1] = add(dp[i][j][l ^ 1], dp[i - 1][j][l]);
                            dp[i][j][l ^ 2] = add(dp[i][j][l ^ 2], dp[i - 1][j][l]);
                            if (j + 2 < K) {
                                dp[i][j + 2][l ^ 3] = add(dp[i][j + 2][l ^ 3], dp[i - 1][j][l]);
                            }
                        }
                    }
                }
            }
            long ans = 0;
            for (int i = 0; i < 4; ++i)
                ans = add(ans, dp[n - 1][K - 1][i]);
            out.println(ans);
        }

        private long add(long a, long b) {
            if (a >= MODULO) a %= MODULO;
            if (b >= MODULO) b %= MODULO;
            return (a + b) % MODULO;
        }

    }

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

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

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

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

    }
}

