E869120 defined a sequence $a$ like this:


* $a_1=a_2=1$, $a_{k+2}=a_{k+1}+a_k \ (k \ge 1)$


He also defined sequences $d_1, d_2, d_3, \dots , d_n$, as the following recurrence relation :


* $d_{1, j} = a_j$
* $d_{i, j} = \sum_{k = 1}^j d_{i - 1, k} \ (i \ge 2)$


You are given integers $n$ and $m$. Please calculate the value of $d_{n, m}$.
Since the answer can be large number, print the answer modulo $998,244,353$.
Can you solve this problem???

Input

The input is given from standard input in the following format.



> $n \quad m$

Output

* Print $d_{n, m}$ modulo $998,244,353$.



Constraints

* $1 \le n \le 200,000$
* $1 \le m \le 10^{18}$



Subtasks

Subtask 1 [ $100$ points ]


* The testcase in this subtask satisfies $1 \le n, m \le 3,000$.

Subtask 2 [ $170$ points ]


* The testcase in this subtask satisfies $1 \le m \le 200,000$.

Subtask 3 [ $230$ points ]


* The testcase in this subtask satisfies $1 \le n \le 3$.

Subtask 4 [ $420$ points ]


* The testcase in this subtask satisfies $1 \le n \le 1000$.

Subtask 5 [ $480$ points ]


* There are no additional constraints.

Output

* Print $d_{n, m}$ modulo $998,244,353$.



Constraints

* $1 \le n \le 200,000$
* $1 \le m \le 10^{18}$



Subtasks

Subtask 1 [ $100$ points ]


* The testcase in this subtask satisfies $1 \le n, m \le 3,000$.

Subtask 2 [ $170$ points ]


* The testcase in this subtask satisfies $1 \le m \le 200,000$.

Subtask 3 [ $230$ points ]


* The testcase in this subtask satisfies $1 \le n \le 3$.

Subtask 4 [ $420$ points ]


* The testcase in this subtask satisfies $1 \le n \le 1000$.

Subtask 5 [ $480$ points ]


* There are no additional constraints.

Input

The input is given from standard input in the following format.



> $n \quad m$

Examples

Input

4 7


Output

176


Input

12 20


Output

174174144


Input

16 30


Output

102292850
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <iostream>
#define maxn 500009
using namespace std;
const int MOD=998244353;
struct Matrix{
	long long a[2][2];
	Matrix operator *(const Matrix &rhs)const{
		Matrix res;
		for(int i=0;i<2;i++)
			for(int j=0;j<2;j++)
				res.a[i][j]=0;
		for(int i=0;i<2;i++)
			for(int j=0;j<2;j++)
				for(int k=0;k<2;k++){
					res.a[i][j]+=a[i][k]*rhs.a[k][j];
					res.a[i][j]%=MOD;
				}
		return res;
	}
	void output(){
		for(int i=0;i<2;i++){
			for(int j=0;j<2;j++)
				cout<<a[i][j]<<" ";
			puts("");
		}
	}
};
long long mgml(long long a,long long b){
	long long res=1;
	a%=MOD;
	while(b){
		if(b&1)
			res=res*a%MOD;
		a=a*a%MOD;
		b>>=1;
	}
	return res;
}
Matrix matrix_mgml(long long b){
	Matrix res;
	for(int i=0;i<2;i++)
		for(int j=0;j<2;j++)
			if(i==j)
				res.a[i][j]=1;
			else
				res.a[i][j]=0;
	Matrix a;
	a.a[0][0]=a.a[0][1]=a.a[1][0]=1;
	a.a[1][1]=0;
	while(b){
		if(b&1)
			res=res*a;
		a=a*a;
		b>>=1;
	}
	return res;
}
long long fib(long long n){
	if(n==0)
		return 0;
	if(n<=2)
		return 1;
	else{
		Matrix M=matrix_mgml(n-2);
		return (M.a[0][0]+M.a[0][1])%MOD;
	}
}
long long comb(long long n,int m){
	long long ans=1;
	n%=MOD;
	for(int i=0;i<m;i++)
		ans=ans*(n-i)%MOD;
	for(int i=1;i<=m;i++)
		ans=ans*mgml(i,MOD-2)%MOD;
	ans+=MOD;
	ans%=MOD;
	return ans;
}
int main(){
	int n;long long m;
	cin>>n>>m;
	if(n==1){
		cout<<fib(m)<<endl;
	}
	else{
		long long ans=0;
		long long C=comb(m+n-3,n-2);
		for(int i=2;i<=n;i++){
			ans-=fib(2*i-2)*C%MOD;
			ans%=MOD;
			C=C*(n-i)%MOD*mgml(m+n-i-1,MOD-2)%MOD;
		}
		ans=ans+fib(m+2*(n-1))%MOD;
		ans+=MOD;
		ans%=MOD;
		cout<<ans<<endl;
	}
	//system("pause");
	return 0;
}