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.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
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;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DBicolorings solver = new DBicolorings();
        solver.solve(1, in, out);
        out.close();
    }

    static class DBicolorings {
        int n;
        int k;
        int mod;
        long[][][] memo;

        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            n = sc.nextInt();
            k = sc.nextInt();
            long ans = 0;
            mod = 998244353;
            memo = new long[1 << 2][n][k + 1];
            for (long[][] x : memo)
                for (long[] y : x)
                    Arrays.fill(y, -1);
            for (int i = 0; i < 1 << 2; i++) {
                ans += dp(1, i, k - (i == 0 || i == (1 << 2) - 1 ? 1 : 2));
                ans %= mod;
            }
            pw.print(ans);
        }

        private long dp(int idx, int msk, int k) {
            if (k < 0)
                return 0;
            if (idx == n)
                return k == 0 ? 1 : 0;
            if (memo[msk][idx][k] != -1)
                return memo[msk][idx][k];
            long ans = 0;
            for (int i = 0; i < 1 << 2; i++) {
                int min = get(msk, i);
                ans += dp(idx + 1, i, k - min);
                ans %= mod;
            }
            return memo[msk][idx][k] = ans;
        }

        private int get(int msk, int msk2) {
            if ((msk2 & 1) == (msk2 >> 1 & 1)) {
                if ((msk & 1) == (msk2 >> 1 & 1) || (msk >> 1 & 1) == (msk2 >> 1 & 1))
                    return 0;
                return 1;
            } else {
                int toRet = 0;
                if ((msk2 & 1) != (msk & 1) && ((msk2 & 1) != (msk2 >> 1 & 1) || (msk2 >> 1 & 1) != (msk >> 1 & 1)))
                    toRet++;
                if ((msk2 >> 1 & 1) != (msk >> 1 & 1) && ((msk2 >> 1 & 1) != (msk2 & 1) || (msk2 & 1) != (msk & 1)))
                    toRet++;
                return toRet;
            }
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

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

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

    }
}

