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 E1066 {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
    }

    static class InputReader {
        StringTokenizer tokenizer;
        InputStreamReader sReader;
        BufferedReader reader;

        InputReader(InputStream stream) {
            sReader = new InputStreamReader(stream);
            reader = new BufferedReader(sReader, 32768);
            tokenizer = null;
        }

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

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

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

        public List<Integer> intLine(int size) {
            List<Integer> ls = new ArrayList<>(size);
            for (int i = 0; i < size; i++) {
                ls.add(nextInt());
            }
            return ls;
        }

        int nextC() {
            try {
                return reader.read();
            } catch (IOException e) {
                return -1;
            }
        }

        public int[] intArr(int size) {
            int[] ls = new int[size];
            for (int i = 0; i < size; i++) ls[i] = nextInt();
            return ls;
        }
    }

    private static class Solver {
        int[][] ans = new int[][]{{0, 0, 0, 1}, {1, 0, 2, 1}, {1, 2, 0, 1}, {1, 0, 0, 0}};
        long[][][] dp = new long[1002][2004][4];
        long mod = 998244353;
        private void solve(InputReader inp, PrintWriter out) {
            dp[0][0] = new long[]{1,1,1,1};
            int n = inp.nextInt(), k =inp.nextInt();
            for (int i=0;i<n;i++){
                for (int j=0;j<k+1;j++){
                    for (int a=0;a<4;a++){
                        for (int b=0;b<4;b++){
                            int j2=j+ans[a][b];
                            dp[i+1][j2][b] = (dp[i+1][j2][b] + dp[i][j][a]) % mod;
                        }
                    }
                }
            }
            long res = 0;
            for (int i=0;i<4;i++){
                int added = ans[i][i^3];
                if (k>=added){
                    res = (dp[n-1][k-added][i]+res)%mod;
                }
            }
//            printer(dp);
            out.println(res%mod);
        }
        public void printer(long[][][] arr){
            long[][] x;
            long[] y;
            for (int i =0; i< 10;i++){
                x=arr[i];
                StringBuilder sb = new StringBuilder("[");
                for (int j=0;j<10;j++) {
                    y=x[j];
                    sb.append("[");
                    for (long l : y) {
                        sb.append(l).append(", ");
                    }
                    sb.replace(sb.length()-2, sb.length(),"]");
                }
                sb.replace(sb.length()-2, sb.length(),"]");
                System.out.println(sb);
            }
        }
    }
}
