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;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        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 mod = 998244353;
            long[][][] dp = new long[n + 1][4][k + 2];
            dp[1][0][1] = 1;
            dp[1][1][2] = 1;
            dp[1][2][2] = 1;
            dp[1][3][1] = 1;
            for (int i = 2; i <= n; i++) {
                for (int j = 0; j <= k; j++) {
                    dp[i][0][j] = (dp[i][0][j] + dp[i - 1][0][j]) % mod;
                    dp[i][0][j] = (dp[i][0][j] + dp[i - 1][1][j]) % mod;
                    dp[i][0][j] = (dp[i][0][j] + dp[i - 1][2][j]) % mod;
                    if (j - 1 >= 0) dp[i][0][j] = (dp[i][0][j] + dp[i - 1][3][j - 1]) % mod;


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


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


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


                }
            }
            long ans = 0;
            for (int i = 0; i < 4; i++) {
                ans = (ans + dp[n][i][k]) % mod;
            }
            while (ans < 0) ans += mod;
            out.println(ans);

        }

    }

    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 integer = 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') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

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

    }
}

