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.io.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jenish
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(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, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int k = in.scanInt();
            long dp[][][] = new long[n + 1][(2 * n) + 5][4];
            long mod = 998244353;

            dp[1][1][0] = 1;
            dp[1][1][1] = 0;
            dp[1][1][2] = 0;
            dp[1][1][3] = 1;
            dp[1][2][0] = 0;
            dp[1][2][1] = 1;
            dp[1][2][2] = 1;
            dp[1][2][3] = 0;

            for (int i = 2; i <= n; i++) {
                for (int j = 1; j <= 2 * i; j++) {
                    dp[i][j][0] += dp[i - 1][j][0];
                    dp[i][j][0] += dp[i - 1][j][1];
                    dp[i][j][0] += dp[i - 1][j][2];
                    dp[i][j][0] += dp[i - 1][j - 1][3];
                    dp[i][j][0] %= mod;

                    dp[i][j][1] += dp[i - 1][j - 1][0];
                    dp[i][j][1] += dp[i - 1][j][1];
                    if (j - 2 >= 0) dp[i][j][1] += dp[i - 1][j - 2][2];
                    dp[i][j][1] += dp[i - 1][j - 1][3];
                    dp[i][j][1] %= mod;


                    dp[i][j][2] += dp[i - 1][j - 1][0];
                    if (j - 2 >= 0) dp[i][j][2] += dp[i - 1][j - 2][1];
                    dp[i][j][2] += dp[i - 1][j][2];
                    dp[i][j][2] += dp[i - 1][j - 1][3];
                    dp[i][j][2] %= mod;


                    dp[i][j][3] += dp[i - 1][j - 1][0];
                    dp[i][j][3] += dp[i - 1][j][1];
                    dp[i][j][3] += dp[i - 1][j][2];
                    dp[i][j][3] += dp[i - 1][j][3];
                    dp[i][j][3] %= mod;
                }
            }


            out.println((dp[n][k][0] + dp[n][k][1] + dp[n][k][2] + dp[n][k][3]) % mod);


        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int INDEX;
        private BufferedInputStream in;
        private int TOTAL;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (INDEX >= TOTAL) {
                INDEX = 0;
                try {
                    TOTAL = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (TOTAL <= 0) return -1;
            }
            return buf[INDEX++];
        }

        public int scanInt() {
            int I = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    I *= 10;
                    I += n - '0';
                    n = scan();
                }
            }
            return neg * I;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}

