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;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            int K = in.nextInt();
            int mod = 998244353;

            int[][][] dp = new int[2 * N + 1][2][2];
            dp[1][0][0] = 1;
            dp[2][0][1] = 1;
            dp[2][1][0] = 1;
            dp[1][1][1] = 1;
            for (int i = 1; i < N; i++) {
                int[][][] ndp = new int[2 * N + 1][2][2];
                for (int k = 0; k <= 2 * N; k++) {
                    for (int i1 = 0; i1 < 2; i1++) {
                        for (int j1 = 0; j1 < 2; j1++) {
                            for (int i2 = 0; i2 < 2; i2++) {
                                for (int j2 = 0; j2 < 2; j2++) {
                                    int dk = (i1 != i2 ? 1 : 0) + (j1 != j2 ? 1 : 0);
                                    if (dk > 0 && i2 == j2)
                                        --dk;
                                    if (k + dk <= K) {
                                        ndp[k + dk][i2][j2] = (ndp[k + dk][i2][j2] + dp[k][i1][j1]) % mod;
                                    }
                                }
                            }
                        }
                    }
                }
                dp = ndp;
            }

            int res = 0;
            for (int i = 0; i < 2; i++) {
                for (int j = 0; j < 2; j++) {
                    res = (res + dp[K][i][j]) % mod;
                }
            }
            out.println(res);
        }

    }

    static class InputReader {
        final InputStream is;
        final byte[] buf = new byte[1024];
        int pos;
        int size;

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

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

        int read() {
            if (size == -1)
                throw new InputMismatchException();
            if (pos >= size) {
                pos = 0;
                try {
                    size = is.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (size <= 0)
                    return -1;
            }
            return buf[pos++] & 255;
        }

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

    }
}

