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;
inline int read()
{
	int x=0,f=1;
	char ch;
	do
	{
		ch=getchar();
		if (ch=='-')
		{
			f=-f;
		}
	}while (ch<'0' || ch>'9');
	do
	{
		x=x*10+ch-'0';
		ch=getchar();
	}while (ch>='0' && ch<='9');
	return x*f;
}
#define ll long long
const int maxn=6010;
const ll Mod=998244353;
int n,k;
ll f[maxn][maxn],inv[maxn],fac[maxn];
void upd(ll &x,ll v)
{
	x=(x+v)%Mod;
}
ll c(int n,int m)
{
	if (m<0 || m>n)
	{
		return 0;
	}
	return fac[n]*inv[m]%Mod*inv[n-m]%Mod;
}
int main()
{
	scanf("%d%d",&n,&k);
	fac[0]=1;
	for (int i=1;i<=n;i++)
	{
		fac[i]=fac[i-1]*i%Mod;
	}
	inv[0]=inv[1]=1;
	for (int i=2;i<=n;i++)
	{
		inv[i]=(Mod-Mod/i)*inv[Mod%i]%Mod;
	}
	for (int i=1;i<=n;i++)
	{
		inv[i]=inv[i]*inv[i-1]%Mod;
	}
	f[0][0]=1;
	for (int i=1;i<=n;i++)
	{
		for (int j=i;j<=i*2;j++)
		{
			upd(f[i][j],f[i-1][j-1]);
			if (j>1)
			{
				upd(f[i][j],f[i-1][j-2]);
			}
		}
	}
	ll ans=0;
	for (int i=0;i<=n;i++)
	{
		ll now=0;
		for (int j=0;j<k-1;j++)
		{
			upd(now,f[i][j]);
		}
		for (int j=0;j<=i;j++)
		{
			if (i-j<=j && k-1-(i-j)*2>=0)
			{
				upd(now,f[j-(i-j)][k-1-(i-j)*2]);
			}
			else if (i-j>j && j*2==k-1)
			{
				upd(now,1);
			}
		}
		upd(ans,now*c(n,i));
	}
	cout<<ans<<endl;
	return 0;
}
