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>

//    #include <boost/multiprecision/cpp_int.hpp>
 #define int long long
 #define inf  1000000007
 #define pa pair<int,int>
 #define ll long long
 #define pal pair<double,double>
 #define ppap pair<pa,int>
  #define PI 3.14159265358979323846
  #define paa pair<int,char>
  #define  mp make_pair
  #define  pb push_back
  #define EPS (1e-10)
                                          
    int dx[8]={0,1,0,-1,1,1,-1,-1};
    int dy[8]={1,0,-1,0,-1,1,1,-1};
                                            using namespace std;
                                   			class pa3{
                                            	public:
                                            	int x;
                                   				int y,z;
                                            	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                            	bool operator < (const pa3 &p) const{
                                            		if(x!=p.x) return x<p.x;
                                            		if(y!=p.y) return y<p.y;
                                            		 return z<p.z;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                   				bool operator > (const pa3 &p) const{
                                            		if(x!=p.x) return x>p.x;
                                            		if(y!=p.y) return y>p.y;
                                            		 return z>p.z;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa3 &p) const{
                                            		return x==p.x && y==p.y && z==p.z;
                                            	}
                                            		bool operator != (const pa3 &p) const{
                                            			return !( x==p.x && y==p.y && z==p.z);
                                            	}
                                            
                                            };
                                            
                                            class pa4{
                                            	public:
                                            	int x;
                                            	int y,z,w;
                                            	pa4(int x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                            	bool operator < (const pa4 &p) const{
                                            		if(x!=p.x) return x<p.x;
                                            		if(y!=p.y) return y<p.y;
                                            		if(z!=p.z)return z<p.z;
                                            		return w<p.w;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator > (const pa4 &p) const{
                                            		if(x!=p.x) return x>p.x;
                                            		if(y!=p.y) return y>p.y;
                                            		if(z!=p.z)return z>p.z;
                                            		return w>p.w;
                                            		//return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa4 &p) const{
                                            		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                            	}
                                            		
                                            
                                            };
                                            class pa2{
                                            	public:
                                            	int x,y;
                                            	pa2(int x=0,int y=0):x(x),y(y) {}
                                            	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                            	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                            	bool operator < (const pa2 &p) const{
                                            		return y != p.y ? y<p.y: x<p.x;
                                            	}
                                            	bool operator > (const pa2 &p) const{
                                            		return x != p.x ? x<p.x: y<p.y;
                                            	}
                                            	bool operator == (const pa2 &p) const{
                                            		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                            	}
                                            	bool operator != (const pa2 &p) const{
                                            		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                            	}
                                            		
                                            
                                            };
                                            

                      
                                string itos( int i ) {
                                ostringstream s ;
                                s << i ;
                                return s.str() ;
                                }
                                 
                                int gcd(int v,int b){
                                	if(v>b) return gcd(b,v);
                                	if(v==b) return b;
                                	if(b%v==0) return v;
                                	return gcd(v,b%v);
                                }
                 
                            
                                int mod;
int extgcd(int a, int b, int &x, int &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    int d = extgcd(b, a%b, y, x);
    y -= a/b * x;
    return d;
}
pa operator+(const pa & l,const pa & r) {   
    return {l.first+r.first,l.second+r.second};                                    
}    
pa operator-(const pa & l,const pa & r) {   
    return {l.first-r.first,l.second-r.second};                                    
}  
                                
                int pr[1200010];
                int inv[1200010];
                
                int beki(int wa,int rr,int warukazu){
                	if(rr==0) return 1%warukazu;
                	if(rr==1) return wa%warukazu;
                	wa%=warukazu;
                	if(rr%2==1) return ((ll)beki(wa,rr-1,warukazu)*(ll)wa)%warukazu;
                	ll zx=beki(wa,rr/2,warukazu);
                	return (zx*zx)%warukazu;
                }

                
    			int comb(int nn,int rr){
    				int r=pr[nn]*inv[rr];
    				r%=mod;
    				r*=inv[nn-rr];
    				r%=mod;
    				return r;
    			}
                
                void gya(int ert){
                	pr[0]=1;
                	for(int i=1;i<=ert;i++){
                		pr[i]=(pr[i-1]*i)%mod;
                	}
                		inv[ert]=beki(pr[ert],mod-2,mod);
                	for(int i=ert-1;i>=0;i--){
                		inv[i]=inv[i+1]*(i+1)%mod;
                	}
                }
                
              //   cin.tie(0);
    		//	ios::sync_with_stdio(false);
    			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
                 //sort(ve.begin(),ve.end(),greater<int>());
//    mt19937(clock_per_sec);
  //  mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()) ;
      
       
       
                               //----------------kokomade tenpure------------



int dp[3100][3100]={};


int yaru(int len,int val){
	if(len==0){
		if(val==0)return 1;
		return 0;
	}
	if(val<len) return 0;
	if(val>2*len) return 0;
	val-=len;
	
	return comb(len,val);
}

int a[3010]={};
 signed main(){
 	

    	       cin.tie(0);
   			ios::sync_with_stdio(false);
mod=998244353;
 	
 	int n,x;
 	cin>>n>>x;
	
 	gya(10000);
 	
 	if(x==1){
 		cout<<beki(2,n,mod)<<endl;
 		return 0;
 	}
 	
 	for(int i=0;i<3100 && 2*i<=x-1;i++)for(int j=0;j<3100;j++){
 		if(j<i)continue;
 		if(i==j){
 		//	cout<<" "<<i<<" "<<j<<endl;
 			if(i*2!=x-1) continue;
 			dp[i][j]=1;
 			a[j+1]+=dp[i][j];
 			while(a[j+1]>=mod)a[j+1]-=mod;
 		//	cout<<" "<<i<<endl;
 		}
 		else{
 			int nokori=x-2-2*i;
 			if(nokori<0)continue;
 			if(2*(j-i-1)<nokori) continue;
 			if(j-i-1>nokori)continue;
 			dp[i][j]=yaru(j-i-1,nokori);
 		
// 			cout<<i<<" "<<j<<" "<<" "<<j-i-1<<" "<<nokori<<" "<<dp[i][j]<<endl;
 		
 			a[j+1]+=dp[i][j];
 			while(a[j+1]>=mod)a[j+1]-=mod;
 			a[j+i+1]+=mod-dp[i][j];
 			while(a[j+i+1]>=mod)a[j+i+1]-=mod;
 		}
 //			cout<<j+1<<" "<<j+1+i<<endl;
 	//	for(int k=0;k<=n;k++)cout<<a[k]<<" ";
 	//	cout<<endl;
 	}
 	
 	for(int i=1;i<=n;i++){
 		a[i]+=a[i-1];
 		while(a[i]>=mod)a[i]-=mod;
 	}
 	
 	
 	
 	for(int i=0;i<=n;i++){
 		for(int j=0;j<x;j++){
 			a[i]+=yaru(i,j);
 			if(a[i]>=mod)a[i]-=mod;
 		}
 	}
 	
 	
 	int ans=0;
 	
 	for(int i=0;i<=n;i++){
 		ans+=comb(n,i)*a[i]%mod;
 	}
 	cout<<ans%mod<<endl;
 	return 0;
  }
  