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>
#include<cstdio>
#include<cstring>
using namespace std;
#define N 6006
typedef long long ll;
const int mod=998244353;
inline ll read(){
	ll x=0,f=1;
	char c=getchar();
	while(c<'0'||c>'9'){
		if(c=='-')f=-1;
		c=getchar();
	}
	while(c>='0'&&c<='9'){
		x=(x<<1)+(x<<3)+c-'0';
		c=getchar();
	}
	return x*f;
}
int n,x,ans,fac[N],ifac[N];
int qpow(int a,int b){
	int ans=1;
	while(b){
		if(b&1)ans=1LL*ans*a%mod;
		a=1LL*a*a%mod;
		b>>=1;
	}
	return ans;
}
void init(int n){
	fac[0]=1;
	for(int i=1;i<=n;++i){
		fac[i]=1LL*fac[i-1]*i%mod;
	}
	ifac[n]=qpow(fac[n],mod-2);
	for(int i=n-1;i>=0;--i){
		ifac[i]=1LL*ifac[i+1]*(i+1)%mod;
	}
}
inline int C(int n,int m){
	if(n<0||m<0||n-m<0)return 0;
	return 1LL*fac[n]*ifac[m]%mod*ifac[n-m]%mod;
}
int main(){
	n=read(),x=read();
	if(x==1){
		return !printf("%d\n",qpow(2,n));
	}
	init(max(n,x));
	for(int k=1;k<=n;++k){
		int tmp=0;
		for(int i=k;i<x;++i){
			tmp=(tmp+C(k,i-k))%mod;
		}
		for(int i=1;i<=k-1;++i){
			if(i<=k-i){
				tmp+=(x-1==2*i);
			}
			else{
				int p=x-1-2*(k-i);
				tmp=(tmp+C(2*i-k,p-(2*i-k)))%mod;
			}
		}
		ans=(ans+1LL*C(n,k)*tmp)%mod;
	}
	printf("%d\n",(ans+1)%mod);
	return 0;
}