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.*;

public class CFD {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    private static final long MOD = 1000L * 1000L * 1000L + 7;
    private static final int[] dx = {0, -1, 0, 1};
    private static final int[] dy = {1, 0, -1, 0};
    private static final String yes = "Yes";
    private static final String no = "No";

    void solve() throws IOException {
        int n = nextInt();
        int k = nextInt();
        long mod = 998244353L;
        long[][] dp = new long[1 + 2 * n][4];
        dp[1][0] = 1;
        dp[2][1] = 1;
        dp[2][2] = 1;
        dp[1][3] = 1;

        for (int p = 2; p <= n; p++) {
            long[][] nxt = new long[1 + 2 * n][4];
            for (int i = 0; i < 1 + 2 * n; i++) {
                for (int j = 0; j < 4; j++) {
                    if (dp[i][j] == 0) {
                        continue;
                    }

                    for (int nj = 0; nj < 4; nj++) {
                        if (nj == 0 || nj == 3) {
                            if ((j ^ nj) == 3) {
                                nxt[1 + i][nj] += dp[i][j];
                                nxt[1 + i][nj] %= mod;
                            }
                            else {
                                nxt[i][nj] += dp[i][j];
                                nxt[i][nj] %= mod;
                            }
                        }
                        else {
                            if (j == nj) {
                                nxt[i][nj] += dp[i][j];
                                nxt[i][nj] %= mod;
                            }
                            else if ((j ^ nj) == 3) {
                                nxt[i + 2][nj] += dp[i][j];
                                nxt[i + 2][nj] %= mod;
                            }
                            else {
                                nxt[i + 1][nj] += dp[i][j];
                                nxt[i + 1][nj] %= mod;
                            }
                        }
                    }
                }
            }

            dp = nxt;
        }

        long res = 0;
        for (int j = 0; j < 4; j++) {
            res += dp[k][j];
            res %= mod;
        }

        outln(res);
    }

    int gcd(int a, int b) {
        while(a != 0 && b != 0) {
            int c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    private void formatPrint(double val) {
        outln(String.format("%.9f%n", val));
    }
    public CFD() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFD();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}