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 java.math.*;

public class Main {
    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        //Scanner sc = new Scanner();
        Reader in = new Reader();
        Main solver = new Main();
        solver.solve(out, in);
        out.flush();
        out.close();

    }
    
    static int maxn = (int)1e4+1;
    static int mod = 998244353;
    static int t,n,q,l;
    static long T,pow[];
    static int[] arr,a,b,x,y;
    static long[][][] dp;
    static boolean vis[];
    static ArrayList<Node> adj[];
    
    void solve(PrintWriter out, Reader in) throws IOException{
        int n = in.nextInt();
        int k = in.nextInt();
        
        
        dp = new long[n+1][4][k+2];
        dp[1][0][1]=1L;
        dp[1][1][1]=1L;
        dp[1][2][2]=1L;
        dp[1][3][2]=1L;
        
        for(int i=2;i<=n;i++){
            dp[i][0][1] = 1;
            dp[i][1][1] = 1;
            
            for(int j=2;j<=k;j++){
                dp[i][0][j] = (dp[i-1][0][j]+dp[i-1][1][j-1]+dp[i-1][2][j]+dp[i-1][3][j])%mod;
                dp[i][1][j] = (dp[i-1][1][j]+dp[i-1][0][j-1]+dp[i-1][2][j]+dp[i-1][3][j])%mod;
                dp[i][2][j] = (dp[i-1][2][j]+dp[i-1][0][j-1]+dp[i-1][1][j-1]+dp[i-1][3][j-2])%mod;
                dp[i][3][j] = (dp[i-1][3][j]+dp[i-1][0][j-1]+dp[i-1][1][j-1]+dp[i-1][2][j-2])%mod;
            }
        }
        
        long ans = 0L;
        for(int i=0;i<4;i++) ans += dp[n][i][k];
        ans%=mod;
        out.println(ans);
        
        
        
    }
    
    
    
    static class Node implements Comparable<Node>{
        int t,w;
        Node(int t,int w){
            this.t = t;
            this.w = w;
        }
        
        
        public int compareTo(Node o){
            return this.t-o.w;
        }
    }
    
    static class Reader {
 
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
     
        public Reader() {
            this(System.in);
        }
     
        public Reader(InputStream is) {
            mIs = is;
        }
     
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
        
        }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
     
        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }
     
        public String next() {
            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 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 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 boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
 
    }
}