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.util.*;
import java.io.*;

import static java.lang.Math.*;

public class EduCfs51D {
    static final long MOD = 998244353L;
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        StringBuilder sb = new StringBuilder();
        int n = sc.nextInt();
        int c = sc.nextInt();
        int[][] colorings = {{0, 1}, {1, 0}, {0, 0}, {1, 1}};
        int[][] append = new int[4][4];
        int thirddir = n*2+10;
        long[][][] dp = new long[4][n+1][thirddir];
        for (int i = 0; i < 4; i++) {
            int[][] grid1 = new int[1][2];
            grid1[0] = colorings[i];
            int from = getComponents(grid1);
            dp[i][0][getComponents(grid1)]++;
            for (int j = 0; j < 4; j++) {
                int[][] grid2 = new int[2][2];
                grid2[0] = colorings[i];
                grid2[1] = colorings[j];
                int to = getComponents(grid2);
                append[i][j] = to - from;
            }
        }
        for (int i = 1; i < n; i++) {
            for (int from = 0; from < 4; from++) {
                for (int to = 0; to < 4; to++) {
                    for (int comp = 0; comp < thirddir; comp++) {
                        int newComp = comp + append[from][to];
                        if (newComp < thirddir) {
                            dp[to][i][newComp] += dp[from][i - 1][comp];
                            dp[to][i][newComp] %= MOD;
                        }
                    }
                }
            }
        }
        long sum = 0L;
        for (int to = 0; to < 4; to++) {
            sum += dp[to][n-1][c];
            sum %= MOD;
        }
        sb.append(sum);

        System.out.print(sb);
    }
    static int getComponents(int[][] arr) {
        boolean[][] visited = new boolean[arr.length][arr[0].length];
        Queue<int[]> q = new ArrayDeque<>();
        int comps = 0;
        for (int i =0; i < arr.length; i++) {
            for (int j = 0; j < arr[0].length; j++) {
                if (!visited[i][j]) {
                    comps++;
                    visited[i][j] = true;
                    q.add(new int[] {i, j});
                    while (!q.isEmpty()) {
                        int[] curr = q.poll();
                        for (int[] dir : dirs) {
                            int r = curr[0] + dir[0];
                            int c = curr[1] + dir[1];
                            if (inBounds(r, c, arr) && !visited[r][c] && arr[r][c] == arr[i][j]) {
                                visited[r][c] = true;
                                q.add(new int[] {r, c});
                            }
                        }
                    }

                }
            }
        }
        return comps;
    }
    static int[][] dirs = {{-1, 0}, {1, 0} , {0, 1}, {0, -1}};
    static boolean inBounds(int i, int j, int[][] arr) {
        return 0 <= i && i < arr.length && 0 <= j && j < arr[0].length;
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(new InputStreamReader(System.in));
        }

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

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

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

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

        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

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

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