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.*;
import java.util.Arrays;
import java.util.StringJoiner;
import java.util.StringTokenizer;
import java.util.function.Function;

public class Main {

    static int N, K;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        K = sc.nextInt();

        System.out.println(solve());
    }

    static int MOD = 998244353;

    static int solve() {

        int[][][][] dp = new int[N+1][2][2][K+3];
        dp[1][0][0][1] = 1;
        dp[1][0][1][2] = 1;
        dp[1][1][0][2] = 1;
        dp[1][1][1][1] = 1;

        for (int i = 1; i < N; i++) {
            for (int k = 0; k <= K; k++) {
                // enum 4*4 wtf
                {
                    int ww = dp[i][0][0][k];
                    dp[i+1][0][0][k] += ww;
                    dp[i+1][0][0][k] %= MOD;

                    dp[i+1][0][1][k+1] += ww;
                    dp[i+1][0][1][k+1] %= MOD;

                    dp[i+1][1][0][k+1] += ww;
                    dp[i+1][1][0][k+1] %= MOD;

                    dp[i+1][1][1][k+1] += ww;
                    dp[i+1][1][1][k+1] %= MOD;
                }

                {
                    int wb = dp[i][0][1][k];
                    dp[i+1][0][0][k] += wb;
                    dp[i+1][0][0][k] %= MOD;

                    dp[i+1][0][1][k] += wb;
                    dp[i+1][0][1][k] %= MOD;

                    dp[i+1][1][0][k+2] += wb;
                    dp[i+1][1][0][k+2] %= MOD;

                    dp[i+1][1][1][k] += wb;
                    dp[i+1][1][1][k] %= MOD;
                }

                {
                    int bw = dp[i][1][0][k];
                    dp[i+1][0][0][k] += bw;
                    dp[i+1][0][0][k] %= MOD;

                    dp[i+1][0][1][k+2] += bw;
                    dp[i+1][0][1][k+2] %= MOD;

                    dp[i+1][1][0][k] += bw;
                    dp[i+1][1][0][k] %= MOD;

                    dp[i+1][1][1][k] += bw;
                    dp[i+1][1][1][k] %= MOD;
                }
                {
                    int bb = dp[i][1][1][k];
                    dp[i+1][0][0][k+1] += bb;
                    dp[i+1][0][0][k+1] %= MOD;

                    dp[i+1][0][1][k+1] += bb;
                    dp[i+1][0][1][k+1] %= MOD;

                    dp[i+1][1][0][k+1] += bb;
                    dp[i+1][1][0][k+1] %= MOD;

                    dp[i+1][1][1][k] += bb;
                    dp[i+1][1][1][k] %= MOD;
                }
            }
        }

        int ans = 0;
        for (int f = 0; f < 2; f++) {
            for (int d = 0; d < 2; d++) {
                ans += dp[N][f][d][K];
                ans %= MOD;
            }
        }
        return ans;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }

    static <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }
}
