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>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define SZ(x) ((int)x.size())
#define FOR(i,a,b) for (int i=a;i<=b;++i)
#define FORD(i,a,b) for (int i=a;i>=b;--i)
using namespace std;
typedef long long LL;
typedef pair<int,int> pa;
typedef vector<int> vec;
void getint(int &v){
    char ch,fu=0;
    for(ch='*'; (ch<'0'||ch>'9')&&ch!='-'; ch=getchar());
    if(ch=='-') fu=1, ch=getchar();
    for(v=0; ch>='0'&&ch<='9'; ch=getchar()) v=v*10+ch-'0';
    if(fu) v=-v;
}
const int MO=998244353;
int n,x;
LL ans,fac[100010],inv[100010];
LL pw(LL x,LL y){
	LL t=1;
	for (;y;y>>=1){
		if (y&1) t=t*x%MO;
		x=x*x%MO;
	}
	return t;
}
LL C(int x,int y){
	return fac[x]*inv[y]%MO*inv[x-y]%MO;
}
LL cal(int x,int y){
	if (y<x || y>x*2) return 0ll;
	return C(x,y-x);
}
int main(){
	fac[0]=1;
	FOR(i,1,100000) fac[i]=fac[i-1]*i%MO;
	inv[100000]=pw(fac[100000],MO-2);
	FORD(i,99999,0) inv[i]=inv[i+1]*(i+1)%MO;
	cin>>n>>x;
	ans=1;
	FOR(m,1,n){
		LL t=0;
		FOR(j,0,x-1) (t+=cal(m,j))%=MO;
		FOR(i,0,m-1){
		//	<=i >=m-i+1
			if (m-i+1<=i) (t+=cal(i+i-m,x-1-(m-i)*2))%=MO;
			else if (i*2==x-1) (++t)%=MO;
		}
		(ans+=t*C(n,m))%=MO;
	}
	ans=(ans%MO+MO)%MO;
	cout<<ans<<endl;
	return 0;
}