Find the number, modulo 998244353, of sequences of length N consisting of 0, 1 and 2 such that none of their contiguous subsequences totals to X.

Constraints

* 1 \leq N \leq 3000
* 1 \leq X \leq 2N
* N and X are integers.

Input

Input is given from Standard Input in the following format:


N X


Output

Print the number, modulo 998244353, of sequences that satisfy the condition.

Examples

Input

3 3


Output

14


Input

8 6


Output

1179


Input

10 1


Output

1024


Input

9 13


Output

18402


Input

314 159


Output

459765451
#include <iostream>
using namespace std;
typedef long long ll;

const ll M=3005,mod=998244353;
ll n,m,res=0,C[M][M];

int main(){
	cin>>n>>m;
	C[0][0]++;
	for(int i=0;i<M-1;i++) for(int j=0;j<=i;j++){
		(C[i+1][j]+=C[i][j])%=mod;
		(C[i+1][j+1]+=C[i][j])%=mod;
	}
	for(int i=0;i<m;i++) for(int j=0;j<=i/2;j++) if(i-j<=n) (res+=C[n][j]*C[n-j][i-2*j])%=mod;
	for(int i=m+1;i<=2*m-2;i+=2){
		int t=(i-m+1)/2*2,x=i-2*t;
		for(int j=0;j<=x/2;j++) if(t+x-j<=n) (res+=C[x-j][j]*C[n][t+x-j])%=mod;
	}
	if(m%2==1) for(int i=m;i<=n;i++) (res+=C[n][i])%=mod;
	cout<<res<<endl;
}