#include<bits/stdc++.h>
using namespace std;

typedef long long lint;
typedef long double louble;

template<typename T1,typename T2> inline T1 max(T1 a,T2 b){return a<b?b:a;}
template<typename T1,typename T2> inline T1 min(T1 a,T2 b){return a<b?a:b;}

namespace ae86
{
	const int bufl = 1<<15;
	
	char buf[bufl],*s=buf,*t=buf;
	
	inline int fetch()
	{
		if(s==t){t=(s=buf)+fread(buf,1,bufl,stdin);if(s==t)return EOF;}
		return *s++;
	}
	
	inline int ty()
	{
		int a=0,b=1,c=fetch();
		while(!isdigit(c))b^=c=='-',c=fetch();
		while(isdigit(c))a=a*10+c-48,c=fetch();
		return b?a:-a;
	}
}
using ae86::ty;

const int _ = 2500007 , mo = 998244353;

inline lint powa(lint a,lint t)
{
	lint b=1;
	while(t){if(t&1)b=b*a%mo;a=a*a%mo,t>>=1;}
	return b;
}

inline lint inva(lint a){return powa(a,mo-2);}

lint jc[_],rjc[_];

inline void fuck(int n=_-1)
{
	jc[0]=jc[1]=rjc[0]=1;
	for(int i=2;i<=n;i++)jc[i]=jc[i-1]*i%mo;
	rjc[n]=inva(jc[n]);
	for(int i=n-1;i>=1;i--)rjc[i]=rjc[i+1]*(1ll+i)%mo;
}

inline lint C(int n,int m)
{
	if(n<m || n<0 || m<0)return 0;
	return jc[n]*rjc[m]%mo*rjc[n-m]%mo;
}

int n,m;

int main()
{
	fuck();

	n=ty(),m=ty();
	lint ans=C(n-1+m+m+m,n-1);
	for(int i=0;i<m;i++)ans=(ans-C(i+n-2,n-2)*n%mo+mo)%mo;
	for(int i=m+1;i<=n;i++)if((m+m+m-i)%2==0)ans=(ans-C(n,i)*C((m+m+m-i)/2+n-1,n-1)%mo+mo)%mo;
	printf("%lld\n",ans);

	return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

We have a sequence of N integers: x=(x_0,x_1,\cdots,x_{N-1}). Initially, x_i=0 for each i (0 \leq i \leq N-1).

Snuke will perform the following operation exactly M times:

* Choose two distinct indices i, j (0 \leq i,j \leq N-1,\ i \neq j). Then, replace x_i with x_i+2 and x_j with x_j+1.



Find the number of different sequences that can result after M operations. Since it can be enormous, compute the count modulo 998244353.

Constraints

* 2 \leq N \leq 10^6
* 1 \leq M \leq 5 \times 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M


Output

Print the number of different sequences that can result after M operations, modulo 998244353.

Examples

Input

2 2


Output

3


Input

3 2


Output

19


Input

10 10


Output

211428932


Input

100000 50000


Output

3463133

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;

typedef long long lint;
typedef long double louble;

template<typename T1,typename T2> inline T1 max(T1 a,T2 b){return a<b?b:a;}
template<typename T1,typename T2> inline T1 min(T1 a,T2 b){return a<b?a:b;}

namespace ae86
{
	const int bufl = 1<<15;
	
	char buf[bufl],*s=buf,*t=buf;
	
	inline int fetch()
	{
		if(s==t){t=(s=buf)+fread(buf,1,bufl,stdin);if(s==t)return EOF;}
		return *s++;
	}
	
	inline int ty()
	{
		int a=0,b=1,c=fetch();
		while(!isdigit(c))b^=c=='-',c=fetch();
		while(isdigit(c))a=a*10+c-48,c=fetch();
		return b?a:-a;
	}
}
using ae86::ty;

const int _ = 2500007 , mo = 998244353;

inline lint powa(lint a,lint t)
{
	lint b=1;
	while(t){if(t&1)b=b*a%mo;a=a*a%mo,t>>=1;}
	return b;
}

inline lint inva(lint a){return powa(a,mo-2);}

lint jc[_],rjc[_];

inline void fuck(int n=_-1)
{
	jc[0]=jc[1]=rjc[0]=1;
	for(int i=2;i<=n;i++)jc[i]=jc[i-1]*i%mo;
	rjc[n]=inva(jc[n]);
	for(int i=n-1;i>=1;i--)rjc[i]=rjc[i+1]*(1ll+i)%mo;
}

inline lint C(int n,int m)
{
	if(n<m || n<0 || m<0)return 0;
	return jc[n]*rjc[m]%mo*rjc[n-m]%mo;
}

int n,m;

int main()
{
	fuck();

	n=ty(),m=ty();
	lint ans=C(n-1+m+m+m,n-1);
	for(int i=0;i<m;i++)ans=(ans-C(i+n-2,n-2)*n%mo+mo)%mo;
	for(int i=m+1;i<=n;i++)if((m+m+m-i)%2==0)ans=(ans-C(n,i)*C((m+m+m-i)/2+n-1,n-1)%mo+mo)%mo;
	printf("%lld\n",ans);

	return 0;
}

```