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;

#define int long long

#define rep(i,n) for(int i=0;i<(n);i++)
#define reps(i,a,b) for(int i=(a);i<(b);i++)
#define pb push_back
#define eb emplace_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second

using vint=vector<int>;
using pint=pair<int,int>;
using vpint=vector<pint>;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}

template<class A,class B>
ostream& operator<<(ostream& ost,const pair<A,B>&p){
	ost<<"{"<<p.first<<","<<p.second<<"}";
	return ost;
}

template<class T>
ostream& operator<<(ostream& ost,const vector<T>&v){
	ost<<"{";
	for(int i=0;i<v.size();i++){
		if(i)ost<<",";
		ost<<v[i];
	}
	ost<<"}";
	return ost;
}

template<uint32_t mod>
struct ModInt{
	uint32_t a;
	ModInt& s(uint32_t vv){
		a=vv<mod?vv:vv-mod;
		return *this;
	}

	ModInt(int64_t x=0){s(x%mod+mod);}

	ModInt& operator+=(const ModInt &x){return s(a+x.a);}
	ModInt& operator-=(const ModInt &x){return s(a+mod-x.a);}
	ModInt& operator*=(const ModInt &x){
		a=uint64_t(a)*x.a%mod;
		return *this;
	}
	ModInt& operator/=(const ModInt &x){
		*this*=x.inv();
		return *this;
	}

	ModInt operator+(const ModInt &x)const{return ModInt(*this)+=x;}
	ModInt operator-(const ModInt &x)const{return ModInt(*this)-=x;}
	ModInt operator*(const ModInt &x)const{return ModInt(*this)*=x;}
	ModInt operator/(const ModInt &x)const{return ModInt(*this)/=x;}
	bool operator==(const ModInt &x)const{return a==x.a;}
	bool operator!=(const ModInt &x)const{return a!=x.a;}
	bool operator<(const ModInt &x)const{return a<x.a;}

	ModInt operator-()const{return ModInt()-*this;}
	ModInt pow(int64_t n)const{
		ModInt res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}

	ModInt inv()const{return pow(mod-2);}
};

template<uint32_t mod>
istream& operator>>(istream& in,ModInt<mod>& a){
	return (in>>a.a);
}
template<uint32_t mod>
ostream& operator<<(ostream& out,const ModInt<mod>& a){
	return (out<<a.a);
}
using mint=ModInt<998244353>;

template<class Mint,int32_t lg>
struct ModIntTable{
	int N;
	vector<Mint>facts,finvs,invs;
	ModIntTable():N(1<<lg),facts(N),finvs(N),invs(N){
		const uint32_t mod=Mint(-1).a+1;
		invs[1]=1;
		for(int i=2;i<N;i++)invs[i]=invs[mod%i]*(mod-mod/i);

		facts[0]=1;
		finvs[0]=1;
		for(int i=1;i<N;i++){
			facts[i]=facts[i-1]*i;
			finvs[i]=finvs[i-1]*invs[i];
		}
	}
	inline Mint fact(int n)const{return facts[n];}
	inline Mint finv(int n)const{return finvs[n];}
	inline Mint inv(int n)const{return invs[n];}
	inline Mint binom(int n,int k)const{return facts[n]*finvs[k]*finvs[n-k];}
	inline Mint perm(int n,int k)const{return facts[n]*finvs[n-k];} 
};
ModIntTable<mint,19>mtable;

int N,X;
mint res[3333];
void calc(){
	res[0]=1;
	for(int i=1;i<=N;i++){
		res[i]=res[i-1]*2;
		for(int j=max(X-2,0ll);j<X;j++){
			if(j<i-1||(i-1)*2<j)continue;
			mint w=mtable.binom(i-1,j-(i-1));
			for(int k=1;k<=2;k++){
				if(j+k>=X)res[i]-=w;
			}
		}
	}

	for(int i=1;i<=N&&i*2<X;i++){
		int m=X-1-2*i;
		for(int j=(m+1)/2;j<=m;j++){
			int num=2*i+j;
			if(num>N)break;
			res[num]+=mtable.binom(j,m-j);
		}
	}

	if(X&1){
		for(int i=X;i<=N;i++)res[i]+=1;
	}
}

signed main(){
	cin>>N>>X;

	calc();

	mint ans;
	for(int i=0;i<=N;i++)ans+=res[i]*mtable.binom(N,i);
	cout<<ans<<endl;
	return 0;
}