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);
        DBicolorings solver = new DBicolorings();
        solver.solve(1, in, out);
        out.close();
    }

    static class DBicolorings {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), k = in.nextInt();
            int m = 998244353;
            long dp[][] = new long[4][k + 2];
            dp[0][1] = 1;
            dp[3][1] = 1;
            dp[1][2] = 1;
            dp[2][2] = 1;
            for (int i = 1; i < n; i++) {
                long dp1[][] = new long[4][k + 1];
                for (int c = 0; c < 3; c++) {
                    for (int j = 1; j <= k; j++) {
                        dp1[0][j] = (dp1[0][j] + dp[c][j]) % m;
                    }
                }
                for (int j = 1; j + 1 <= k; j++) {
                    dp1[0][j + 1] = (dp1[0][j + 1] + dp[3][j]) % m;
                }
                for (int c = 1; c <= 3; c++) {
                    for (int j = 1; j <= k; j++) {
                        dp1[3][j] = (dp1[3][j] + dp[c][j]) % m;
                    }
                }
                for (int j = 1; j + 1 <= k; j++) {
                    dp1[3][j + 1] = (dp1[3][j + 1] + dp[0][j]) % m;
                }

                for (int j = 1; j + 1 <= k; j++) {
                    dp1[1][j + 1] = (dp1[1][j + 1] + dp[0][j]) % m;
                }
                for (int j = 1; j + 2 <= k; j++) {
                    dp1[1][j + 2] = (dp1[1][j + 2] + dp[1][j]) % m;
                }
                for (int j = 1; j <= k; j++) {
                    dp1[1][j] = (dp1[1][j] + dp[2][j]) % m;
                }
                for (int j = 1; j + 1 <= k; j++) {
                    dp1[1][j + 1] = (dp1[1][j + 1] + dp[3][j]) % m;
                }

                for (int j = 1; j + 1 <= k; j++) {
                    dp1[2][j + 1] = (dp1[2][j + 1] + dp[0][j]) % m;
                }
                for (int j = 1; j <= k; j++) {
                    dp1[2][j] = (dp1[2][j] + dp[1][j]) % m;
                }
                for (int j = 1; j + 2 <= k; j++) {
                    dp1[2][j + 2] = (dp1[2][j + 2] + dp[2][j]) % m;
                }
                for (int j = 1; j + 1 <= k; j++) {
                    dp1[2][j + 1] = (dp1[2][j + 1] + dp[3][j]) % m;
                }
                dp = dp1;
            }
            long sum = 0;
            for (int i = 0; i < 4; i++) {
                sum = (sum + dp[i][k]) % m;
            }
            out.println(sum);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

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

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

