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;

const int N=3000,mod=998244353;

int add(int a,int b,int p=mod){return a+b>=p?a+b-p:a+b;}
int sub(int a,int b,int p=mod){return a-b<0?a-b+p:a-b;}
int mul(int a,int b,int p=mod){return (LL)a*b%p;}
void sadd(int &a,int b,int p=mod){a=add(a,b,p);}
void ssub(int &a,int b,int p=mod){a=sub(a,b,p);}
void smul(int &a,int b,int p=mod){a=mul(a,b,p);}

int n,m;

void into(){
  scanf("%d%d",&n,&m);
}

int inv[N*2+9],fac[N*2+9],ifac[N*2+9];

void Get_inv(){
  inv[1]=1;
  fac[0]=fac[1]=1;
  ifac[0]=ifac[1]=1;
  for (int i=2;i<=n<<1;++i){
	inv[i]=mul(mod-mod/i,inv[mod%i]);
	fac[i]=mul(fac[i-1],i);
	ifac[i]=mul(ifac[i-1],inv[i]);
  }
}

int Get_c(int n,int m){return n<m||m<0?0:mul(fac[n],mul(ifac[m],ifac[n-m]));}

int Get_ans(int n){
  int res=m&1||n<<1<m;
  for (int i=n;i<n<<1;++i)
	if (i<m) sadd(res,Get_c(n,i-n));
    else if (m-i&1){
	  int p=i-m+1>>1;
	  sadd(res,Get_c(n-p*2,i-p*2-n));
	}
  return res;
}

int ans;

void Get_ans(){
  for (int i=0;i<=n;++i) sadd(ans,mul(Get_c(n,i),Get_ans(i)));
}

void work(){
  Get_inv();
  Get_ans();
}

void outo(){
  printf("%d\n",ans);
}

int main(){
  into();
  work();
  outo();
  return 0;
}