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;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

#define fi first
#define se second
#define repl(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++)
#define rep(i,n) repl(i,0,n)
#define all(x) (x).begin(),(x).end()
#define dbg(x) cout<<#x"="<<x<<endl
#define mmax(x,y) (x>y?x:y)
#define mmin(x,y) (x<y?x:y)
#define maxch(x,y) x=mmax(x,y)
#define minch(x,y) x=mmin(x,y)
#define uni(x) x.erase(unique(all(x)),x.end())
#define exist(x,y) (find(all(x),y)!=x.end())
#define bcnt __builtin_popcountll

#define INF 1e16
#define mod 998244353

ll mod_pow(ll a,ll n){
  ll res=1;
  while(n>0){
    if(n&1)res=res*a%mod;
    a=a*a%mod;
    n>>=1;
  }
  return res;
}

ll fac[100010],finv[100010];
ll comb(ll n,ll r){
  if(n<0||r<0||n<r)return 0;
  else return (fac[n]*finv[r]%mod)*finv[n-r]%mod;
}

ll calc(ll l,ll s){
  return comb(l,s-l);
}

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  fac[0]=1;
  rep(i,100000)fac[i+1]=fac[i]*(i+1)%mod;
  rep(i,100001)finv[i]=mod_pow(fac[i],mod-2);

  ll N,X;
  cin>>N>>X;

  ll res=1;
  repl(len,1,N+1){
    ll add=0;

    rep(s,X){
      add+=calc(len,s);
      add%=mod;
    }

    repl(i,1,(len/2)+1){
      if(i*2<X-1){
        add+=calc(len-2*i,X-1-2*i);
        add%=mod;
        if((X-1-2*i)==2*(len-2*i)){
          add=(add-1+mod)%mod;
          add%=mod;
        }
      }
    }

    if(len*2>=X&&X%2==1){
      add++;
      add%=mod;
    }

    res+=add*comb(N,len)%mod;
    res%=mod;
  }
  cout<<res<<endl;

  return 0;
}
