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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
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[][][] dp = new int[n + 1][2 * n + 3][4];
            dp[1][1][0] = 1;
            dp[1][2][1] = 1;
            dp[1][2][2] = 1;
            dp[1][1][3] = 1;
            for (int i = 2; i <= n; i++) {
                for (int j = 0; j <= k; j++) {
                    //00-00
                    dp[i][j][0] += dp[i - 1][j][0];
                    dp[i][j][0] %= 998244353;
                    //00-01
                    dp[i][j + 1][1] += dp[i - 1][j][0];
                    dp[i][j + 1][1] %= 998244353;
                    //00-10
                    dp[i][j + 1][2] += dp[i - 1][j][0];
                    dp[i][j + 1][2] %= 998244353;
                    //00-11
                    dp[i][j + 1][3] += dp[i - 1][j][0];
                    dp[i][j + 1][3] %= 998244353;
                    //01-00
                    dp[i][j][0] += dp[i - 1][j][1];
                    dp[i][j][0] %= 998244353;
                    //01-01
                    dp[i][j][1] += dp[i - 1][j][1];
                    dp[i][j][1] %= 998244353;
                    //01-10
                    dp[i][j + 2][2] += dp[i - 1][j][1];
                    dp[i][j + 2][2] %= 998244353;
                    //01-11
                    dp[i][j][3] += dp[i - 1][j][1];
                    dp[i][j][3] %= 998244353;
                    //10-00
                    dp[i][j][0] += dp[i - 1][j][2];
                    dp[i][j][0] %= 998244353;
                    //10-01
                    dp[i][j + 2][1] += dp[i - 1][j][2];
                    dp[i][j + 2][1] %= 998244353;
                    //10-10
                    dp[i][j][2] += dp[i - 1][j][2];
                    dp[i][j][2] %= 998244353;
                    //10-11
                    dp[i][j][3] += dp[i - 1][j][2];
                    dp[i][j][3] %= 998244353;
                    //11-00
                    dp[i][j + 1][0] += dp[i - 1][j][3];
                    dp[i][j + 1][0] %= 998244353;
                    //11-01
                    dp[i][j + 1][1] += dp[i - 1][j][3];
                    dp[i][j + 1][1] %= 998244353;
                    //11-10
                    dp[i][j + 1][2] += dp[i - 1][j][3];
                    dp[i][j + 1][2] %= 998244353;
                    //11-11
                    dp[i][j][3] += dp[i - 1][j][3];
                    dp[i][j][3] %= 998244353;
                }
            }
            int ans = 0;
            for (int i = 0; i < 4; i++) {
                ans += dp[n][k][i];
                ans %= 998244353;
            }
            out.println(ans);
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer stt;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        public String next() {
            while (stt == null || !stt.hasMoreTokens()) {
                stt = new StringTokenizer(nextLine());
            }
            return stt.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

