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 javax.swing.plaf.synth.SynthEditorPaneUI;
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Contest1 {
    static int mod=998244353 ,n;
    static int[][][]memo;
    static int dp(int msk,int idx,int rem){
        if (rem<0)
            return 0;
        if (idx==n)
            return rem==0?1:0;
        if (memo[msk][idx][rem]!=-1)
            return memo[msk][idx][rem];
        int ans=0;
        for (int i =0;i<4;i++){
            ans+=dp(i,idx+1,rem-get(msk,i));
            ans%=mod;
        }
        return memo[msk][idx][rem]=ans;
    }
    static int get(int pre,int nxt){
        if (nxt==0){
            if (pre!=3)
                return 0;
            return 1;
        }
        if (nxt==3){
            if (pre!=0)
                return 0;
            return 1;
        }
        int ans=0;
        if ((nxt&1)!=(pre&1))
            ans++;
        nxt>>=1;
        pre>>=1;
        if ((nxt&1)!=(pre&1))
            ans++;
        return ans;
    }
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        n = sc.nextInt();
        int k = sc.nextInt();
        memo= new int[4][n+1][k+1];
        int ans=0;
        for (int[][]x:memo)for (int[]z:x)Arrays.fill(z,-1);
        for (int i =0;i<4;i++){
            ans+=dp(i,1,k-(i==0||i==3?1:2));
            ans%=mod;
        }
        pw.println(ans);
        pw.flush();
    }
    static long gcd(long a,long b){
        if (a==0)
            return b;
        return gcd(b%a,a);
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}