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<string.h>
#include<string>
#include<stdio.h>
#include<algorithm>
#include<math.h>
#include<vector>
#include<queue>
#include<map>
#include<set>
using namespace std;
#define lowbit(x) (x)&(-x)
#define rep(i,a,b) for (int i=a;i<=b;i++)
#define per(i,a,b) for (int i=a;i>=b;i--)
#define maxd 998244353
typedef long long ll;
const int N=3000;
const double pi=acos(-1.0);
int n,x;
ll c[3030][3030];

int read()
{
	int x=0,f=1;char ch=getchar();
	while ((ch<'0') || (ch>'9')) {if (ch=='-') f=-1;ch=getchar();}
	while ((ch>='0') && (ch<='9')) {x=x*10+(ch-'0');ch=getchar();}
	return x*f;
}

void init()
{
	rep(i,0,N)
	{
		c[i][0]=1;
		rep(j,1,i) c[i][j]=(c[i-1][j-1]+c[i-1][j])%maxd;
	}
}

ll solve(int n,int x)
{
	ll ans=0;
	if ((x%2==1) || (2*n<x)) ans=1;
	rep(s,n,2*n-1)
	{
		if (s<x) ans=(ans+c[n][s-n])%maxd;
		else
		{
			if ((s-x)%2==0) continue;
			int lft=(s-x+1)/2;
			if (lft*2<n)
			{
				ll restn=n-2*lft,rests=s-4*lft;
				if ((restn<=rests) && (rests<=2*restn)) ans=(ans+c[restn][rests-restn])%maxd;
			}
		}
	}
	return ans;
}

int main()
{
	init();ll ans=0;
	n=read();x=read();
	rep(i,0,n) ans=(ans+c[n][i]*solve(n-i,x))%maxd;
	printf("%lld",ans);
	return 0;
}
	