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<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int,int> pii;
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define sz(a) int(a.size())
const int N=3e3+10;
const int mod=998244353;

int gi() {
	int x=0,o=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
	return x*o;
}

int n,x,C[N][N];

int getC(int n,int m) {
	if(m<0||n<m) return 0;
	return C[n][m];
}

int cal(int n) {
	int ret=0;
	if(2*n<x||x%2==1) ret=1;
	for(int i=n;i<2*n;i++) {
		if(i<x) ret=(ret+getC(n,i-n))%mod;
		else {
			if(i%2==x%2) continue;
			int cnt=(i-x+1)/2;
			int rp=n-2*cnt,rs=i-4*cnt;
			ret=(ret+getC(rp,rs-rp))%mod;
		}
	}
	return ret;
}

int main() {
	for(int i=0;i<N;i++) {
		C[i][0]=1;
		for(int j=1;j<=i;j++) C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
	}
	cin>>n>>x;
	int ans=0;
	for(int i=0;i<=n;i++) {
		ans=(ans+1ll*getC(n,i)*cal(n-i))%mod;
	}
	cout<<ans;
	return 0;
}
