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.StringTokenizer;


public class Main {
    static final int UNCALC = -1, mod = 998244353;
    static int n, k, memo[][][];

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        n = sc.nextInt();
        k = sc.nextInt();
        memo = new int[4][n][k + 1];
        for (int[][] a : memo)
            for (int[] b : a)
                Arrays.fill(b, UNCALC);
        int ans = 0;
        for (int start = 0; start < 4; start++)
            ans = add(ans, dp(start, 1, k - (start == 0 || start == 3 ? 1 : 2)));
        out.println(ans);
        out.flush();
        out.close();
    }

    static int remove(int prev, int cur) {
        if (prev == 0) return cur == 0 ? 0 : -1;
        if (prev == 1) return cur == 2 ? -2 : 0;
        if (prev == 2) return cur == 1 ? -2 : 0;
        return cur == 3 ? 0 : -1;
    }

    static int dp(int prev, int i, int rem) {
        if (rem < 0) return 0;
        if (i == n) return rem == 0 ? 1 : 0;
        if (memo[prev][i][rem] != UNCALC) return memo[prev][i][rem];
        int cnt = 0;
        for (int cand = 0; cand < 4; cand++) cnt = add(cnt, dp(cand, i + 1, rem + remove(prev, cand)));

        return memo[prev][i][rem] = cnt;
    }

    static int add(int a, int b) {
        long c = a + b;
        if (c >= mod)
            c -= mod;
        return (int) c;
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public Scanner(String s) throws FileNotFoundException {

            br = new BufferedReader(new FileReader(new File(s)));
        }


        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

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

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }


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

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


        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] ans = new double[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextDouble();
            return ans;
        }

        public short nextShort() throws IOException {
            return Short.parseShort(next());
        }

    }

}