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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Comparator;

public class Main extends PrintWriter {

    static BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
    // static Scanner s=new Scanner(System.in);
    Main () { super(System.out); }
    public static void main(String[] args) throws IOException{
        Main  d1=new Main   ();d1.main();d1.flush();
    }
    void main() throws IOException {
        BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
        StringBuffer sb = new StringBuffer();
        StringBuffer sb1 = new StringBuffer();
        PrintWriter out = new PrintWriter(System.out);
        int t=1;
//        t=i(s()[0]);
        while(t-->0) {
            //dp[i]=a[i]+max(dp[j]) S.T. j<i and h[j]<h[i];
            String[] s1=s();
            int n=i(s1[0]);
           int mod=998244353 ;
           int K=i(s1[1]);
            long[] [][][] dp=new long[n][2*n+1][2][2];
           dp[0][2][0][1]=1;
           dp[0][2][1][0]=1;
           dp[0][1][1][1]=1;
           dp[0][1][0][0]=1;
           for(int i=1;i<n;i++){
               for(int k=1;k<=Math.min(2*(i+1),K);k++){
                  dp[i][k][0][0]=(dp[i-1][k][0][1]%mod+dp[i-1][k][1][0]%mod+dp[i-1][k][0][0]%mod+dp[i-1][k-1][1][1]%mod)%mod;
                  dp[i][k][0][1]=(dp[i-1][k][0][1]%mod+dp[i-1][Math.max(k-2,0)][1][0]%mod+dp[i-1][k-1][0][0]%mod+dp[i-1][k-1][1][1]%mod)%mod;
                  dp[i][k][1][0]=(dp[i-1][Math.max(k-2,0)][0][1]%mod+dp[i-1][k][1][0]%mod+dp[i-1][k-1][0][0]%mod+dp[i-1][k-1][1][1]%mod)%mod;
                  dp[i][k][1][1]=(dp[i-1][k][0][1]%mod+dp[i-1][k][1][0]%mod+dp[i-1][k-1][0][0]%mod+dp[i-1][k][1][1]%mod)%mod;
// System.out.println(ans);
//               System.out.println((dp[i][k][0][1]+" "+dp[i][k][0][0]+" "+dp[i][K][1][1]+" "+dp[i][K][1][0]));
            }
           }
            System.out.println((dp[n-1][K][0][1]%mod+dp[n-1][K][0][0]%mod+dp[n-1][K][1][1]%mod+dp[n-1][K][1][0]%mod)%mod+"\n");

        }

    }
    //        System.out.println(sb);
    long[] st;
    void buildtree(int i,int s,int e,long[] a){
        if(s==e){
            st[i]=a[s];
            return;
        }
        int mid=(s+e)/2;
        buildtree(2*i,s,mid,a);
        buildtree(2*i+1,mid+1,e,a);
        st[i]=Math.min(st[2*i],st[2*(i)+1]);
    }
    long query(int i,int s,int e,int qs,int qe){
        if(qs>e||qe<s) return Integer.MIN_VALUE;
        if(s>=qs&&e<=qe) return st[i];
        int mid=(s+e)/2;
        long l=query(2*i,s,mid,qs,qe);
        long r=query(2*i+1,mid+1,e,qs,qe);
        return Math.max(l,r);
    }
    void pointupdate(int i,int s,int e,int qi,long [] a){
        if(s==e){
            st[i]=a[s];return;
        }
        int mid=(s+e)/2;
        if(qi<=mid) pointupdate(2*i,s,mid,qi,a);
        else pointupdate(2*(i)+1,mid+1,e,qi,a);
        st[i]=Math.max(st[2*i],st[2*i+1]);
    }
    public void arr(long[] a,int n) throws IOException{
        //        BufferedReader s = new BufferedReader(new InputStreamReader(System.in));
        String[] s2=s();
        for(int i=0;i<n;i++){
            a[i]=i(s2[i]);
        }
    }
    public void sort(int[] a,int l,int h){
        if(l==h) return;
        int mid=(l+h)/2;

        sort(a,l,mid);
        sort(a,mid+1,h);
        merge(a,l,(l+h)/2,h);
    }
    void merge(int arr[], int l, int m, int r)
    {
        int n1 = m - l + 1;
        int n2 = r - m;
        int L[] = new int[n1];
        int R[] = new int[n2];
        for (int i = 0; i < n1; ++i)
            L[i] = arr[l + i];
        for (int j = 0; j < n2; ++j)
            R[j] = arr[m + 1 + j];
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2) {
            if (L[i] <= R[j]) {
                arr[k] = L[i];
                i++;
            }
            else {
                arr[k] = R[j];
                j++;
            }
            k++;
        }

        while (i < n1) {
            arr[k] = L[i];
            i++;
            k++;
        }
        while (j < n2) {
            arr[k] = R[j];
            j++;
            k++;
        }
    }


    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    static String[] s() throws IOException {
        return s.readLine().trim().split("\\s+");
    }

    static int i(String ss) {
        return Integer.parseInt(ss);
    }
    static long l(String ss) {
        return Long.parseLong(ss);
    }
}
class Student {
    long  a;int b;int c;
    public Student(int a,int b) {
        this.a=a;this.c=c;this.b=b;
    }
}
class Pair {
    int  a,b,c;
    public Pair(int  a,int b){
        this.a=a;this.b=b;this.c=c;}
}
class Sortbyroll implements Comparator<Student> {

    public int compare(Student a, Student b){
        if(a.b==b.b) return (int)b.a-(int)a.a;
        return   a.b-b.b;}
}