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<algorithm>
#include<vector>
#include<queue>
#include<set>
#include<unordered_map>
using namespace std;
typedef long long ll;
#define chmax(a,b) a=max(a,b)
#define chmin(a,b) a=min(a,b)
#define mod 998244353
#define mad(a,b) a=(a+b)%mod
#define N 6010
ll dp[N][N];
ll fac[N],ivf[N],inv[N];
ll C(ll n,ll k){
    return fac[n]*ivf[n-k]%mod*ivf[k]%mod;
}
int main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    fac[0]=ivf[0]=inv[1]=1;
    for(int i=1;i<N;i++){
	if(i>1)inv[i]=(mod-mod/i*inv[mod%i]%mod)%mod;
	fac[i]=fac[i-1]*i%mod;
	ivf[i]=ivf[i-1]*inv[i]%mod;
    }
    ll n,x; cin>>n>>x;
    for(int i=0;i<N;i++)for(int j=0;j<N;j++)dp[i][j]=0;
    dp[0][0]=1;
    for(int i=0;i<n;i++)for(int j=0;j<x;j++){
	mad(dp[i+1][j+1],dp[i][j]);
	mad(dp[i+1][j+2],dp[i][j]);
    }
    ll ans=0;
    for(int i=0;i<=n;i++)for(int j=0;j<x;j++){
	mad(ans,dp[i][j]*C(n,n-i));
    }//cout<<ans<<endl;
    for(int i=x;i<=n;i++){
	if(x%2==1)mad(ans,C(n,n-i));
    }//cout<<ans<<endl;
    for(int p=2;x-p-1>=0;p+=2){
	for(int m=0;m+p<=n;m++){
	    mad(ans,dp[m][x-p-1]*C(n,m+p));
	}
    }
    cout<<ans<<endl;
}


