AT_fps_24_a お菓子

显然设生成函数 \(F(x)=x+x^3+x^4+x^6\)，然后答案就是 \([x^n]F(x)^D\)。

\((x+x^3+x^4+x^6)^D=x^D(1+x^2+x^3+x^5)^D=x^D(1+x^2)^D(1+x^3)^D\)

\([x^n]F(x)^D=[x^{n-D}]((1+x^2)^D(1+x^3)^D)=\sum_i{D\choose i}x^{2i}\cdot \sum_j{D\choose j}x^{3j}[3j+2i=n-D]\)

\(j=\frac{n-D-2i}{3}\)

\([x^n]F(x)^D=\sum_i{D\choose i}{D\choose \frac{n-D-2i}{3}}\)

#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
#define fin(x) freopen(#x".in","r",stdin)
#define fout(x) freopen(#x".out","w",stdout)
#define fr(x) fin(x),fout(x);
#define Fr(x,y) fin(x),fout(y)
#define INPUT(_1,_2,FILE,...) FILE
#define IO(...) INPUT(__VA_ARGS__,Fr,fr)(__VA_ARGS__)
using namespace std;
using namespace __gnu_pbds;
#define mp make_pair
#define pii pair<int,int>
#define fi first
#define se second
#define pb push_back
#define cfast ios::sync_with_stdio(false);cin.tie(0),cout.tie(0)
#define ll long long
#define ull unsigned long long
#define intz(x,y) memset((x),(y),sizeof((x)))
char *p1,*p2,buf[100000];
#define nc() (p1==p2 && (p2=(p1=buf)+fread(buf,1,100000,stdin),p1==p2)?EOF:*p1++)
#define tup(x) array<int,(x)>
inline ll read(){
    ll x=0,f=1;char ch=nc();
    while(ch<48||ch>57){if(ch=='-')f=-1;ch=nc();}
    while(ch>=48&&ch<=57)x=x*10+ch-48,ch=nc();
   	return x*f;
}
//void write(int x){cout<<x<<' ';}
//void write(pii x){cout<<"P("<<x.fi<<','<<x.se<<")\n";}
//void write(vector<auto>x){for(auto i:x)write(i);cout<<'\n';}
//void write(auto *a,int l,int r){for(int i=l;i<=r;i++)write(a[i]);cout<<'\n';}
inline ll lowbit(ll x){return x&-x;}
inline int pcount(ll x){
	for(int i=0,res=0;;res+=(x>>i)&1,i++)
		if(i>60)return res;
}

//struct mt{
//	ll v;
//	mt(){v=0;}
//	mt(int x){this->v=x;}
//	inline mt operator+(mt x){return {(v+x.v)%mod};}
//	inline mt operator-(mt x){return {(v+mod-x.v)%mod};}
//	inline mt operator*(mt x){return {1ll*v*x.v%mod};}
//};
//inline void add(mt &x,mt y){x=x+y;}
//mt qp(mt x,int y){mt res(1);for(;y;x=x*x,y>>=1)if(y&1)res=res*x;return res;}
const int N=2e5+5,mod=998244353;
int fac[N],ifac[N];
int qp(int x,int y){int res=1;for(;y;y>>=1,x=1ll*x*x%mod)if(y&1)res=1ll*res*x%mod;return res;}
int C(int x,int y){return x<y?0:1ll*fac[x]*ifac[y]%mod*ifac[x-y]%mod;}
inline void UesugiErii(){
	int d,n,ans=0;cin>>d>>n;
	fac[0]=ifac[0]=1;
	for(int i=1;i<=d;i++)
		fac[i]=1ll*fac[i-1]*i%mod;
	ifac[d]=qp(fac[d],mod-2);
	for(int i=d;i;i--)
		ifac[i-1]=1ll*ifac[i]*i%mod;
	for(int i=0;i*2<=n-d;i++)
		if(!((n-d-2*i)%3))
			ans=(ans+1ll*C(d,(n-d-2*i)/3)*C(d,i)%mod)%mod;
	cout<<ans;
}
signed main(){
	//IO();//cfast;
	int _=1;//cin>>_;
	for(;_;_--)UesugiErii();
	return 0;
}