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.*;
import java.math.*;
import java.lang.*;
 
import static java.lang.Math.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        
        public int read() {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt() {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
            
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
            
            return res * sgn;
        }
        
        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
        
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        
        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() {
            return readString();
        }
        
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(),"Main",1<<26).start();
    }
    long add(long a, long b) {
        return (a + b) % mod;
    }
    long mod = 998244353;
    public void run() {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);

        int n = sc.nextInt();
        int k = sc.nextInt();

        long dp[][][] = new long[n][k][4];
        
        dp[0][0][0] = 1;
        dp[0][0][3] = 1;

        if(k > 1) {
            dp[0][1][1] = 1;
            dp[0][1][2] = 1;
        }

        for(int i = 1; i < n; ++i) {
            for(int j = 0; j < k; ++j) {
                for(int l = 0; l < 4; ++l) {
                    if(l == 0 || l == 3) {
                        dp[i][j][l] = add(dp[i][j][l], dp[i - 1][j][l]);
                        if(j + 1 < k) {
                            dp[i][j + 1][l ^ 1] = add(dp[i][j + 1][l ^ 1], dp[i - 1][j][l]);
                            dp[i][j + 1][l ^ 2] = add(dp[i][j + 1][l ^ 2], dp[i - 1][j][l]);
                            dp[i][j + 1][l ^ 3] = add(dp[i][j + 1][l ^ 3], dp[i - 1][j][l]);
                        }
                    }
                    else {
                        dp[i][j][l] = add(dp[i][j][l], dp[i - 1][j][l]);
                        dp[i][j][l ^ 1] = add(dp[i][j][l ^ 1], dp[i - 1][j][l]);
                        dp[i][j][l ^ 2] = add(dp[i][j][l ^ 2], dp[i - 1][j][l]);
                        if(j + 2 < k) {
                            dp[i][j + 2][l ^ 3] = add(dp[i][j + 2][l ^ 3], dp[i - 1][j][l]);
                        }
                    }
                }
            }
        }

        long ans = 0;
        for(int i = 0; i < 4; ++i)
            ans = add(ans, dp[n - 1][k - 1][i]);
    
        w.print(ans);

        w.close();
    }
}