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>
/**
 * Created by Baelish on 9/20/2018.
 */

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class D_2 {
    static long dp[][][][] = new long[2][2][1005][2005], n, k, mod = 998244353;

    public static void main(String[] args) throws Exception {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    solveIt();
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
        }, "Main", 1 << 25).start();
    }

    public static void solveIt() throws Exception {
        FastReader in = new FastReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        for (long b[][][] : dp) for (long c[][] : b) for (long d[] : c) Arrays.fill(d, -1);

        n = in.nextInt();
        k = in.nextInt();
        pw.println(solve(1, 0, 0, 0));

        pw.close();
    }

    static long solve(int x, int v, int a, int b) {
        if (v > k) return 0;
        if (x > n) {
            if (v == k) return 1;
            else return 0;
        }
        if (dp[a][b][x][v] != -1) return dp[a][b][x][v];
        else {
            long res = 0;
            if (x == 1) {
                res += solve(x + 1, v + 1, 0, 0);
                res += solve(x + 1, v + 2, 0, 1);
                res += solve(x + 1, v + 2, 1, 0);
                res += solve(x + 1, v + 1, 1, 1);
            } else {
                if (a == 1 && b == 1) {
                    res += solve(x + 1, v + 1, 0, 0);
                    res += solve(x + 1, v + 1, 1, 0);
                    res += solve(x + 1, v + 1, 0, 1);
                    res += solve(x + 1, v, 1, 1);
                }
                if (a == 0 && b == 0) {
                    res += solve(x + 1, v + 1, 1, 1);
                    res += solve(x + 1, v + 1, 1, 0);
                    res += solve(x + 1, v + 1, 0, 1);
                    res += solve(x + 1, v, 0, 0);
                }
                if (a == 1 && b == 0) {
                    res += solve(x + 1, v, 0, 0);
                    res += solve(x + 1, v, 1, 1);
                    res += solve(x + 1, v, 1, 0);
                    res += solve(x + 1, v + 2, 0, 1);
                }
                if (a == 0 && b == 1) {
                    res += solve(x + 1, v + 2, 1, 0);
                    res += solve(x + 1, v, 0, 0);
                    res += solve(x + 1, v, 0, 1);
                    res += solve(x + 1, v, 1, 1);
                }
            }
            res %= mod;
            return dp[a][b][x][v] = res;
        }
    }


    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;

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

        public int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        public String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }


        public String nextLine() {
            int c = skip();
            StringBuilder sb = new StringBuilder();
            while (!isEndOfLine(c)) {
                sb.appendCodePoint(c);
                c = readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public char[] next(int n) {
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        public char readChar() {
            return (char) skip();
        }
    }
}