#943616 (C++14) No.2605 Pickup Parentheses

• 問題: No.2605 Pickup Parentheses
• ユーザー: TairitsuMeow
• 提出日時: 2024-01-12 22:43:23
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 266 ms / 2,000 ms
• コード長: 2,861 bytes
• コンパイル時間: 3,747 ms
• コンパイル使用メモリ: 246,268 KB
• 実行使用メモリ: 27,280 KB
• 最終ジャッジ日時: 2024-09-30 06:27:57
• 合計ジャッジ時間: 9,363 ms
• ジャッジサーバーID （参考情報）: judge1 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	3 ms; 9,808 KB
testcase_01	AC	3 ms; 10,060 KB
testcase_02	AC	3 ms; 10,064 KB
testcase_03	AC	3 ms; 9,956 KB
testcase_04	AC	4 ms; 9,824 KB
testcase_05	AC	4 ms; 9,964 KB
testcase_06	AC	5 ms; 10,100 KB
testcase_07	AC	5 ms; 10,088 KB
testcase_08	AC	6 ms; 10,104 KB
testcase_09	AC	3 ms; 9,948 KB
testcase_10	AC	5 ms; 9,968 KB
testcase_11	AC	4 ms; 9,952 KB
testcase_12	AC	3 ms; 10,072 KB
testcase_13	AC	4 ms; 9,972 KB
testcase_14	AC	4 ms; 9,972 KB
testcase_15	AC	5 ms; 9,852 KB
testcase_16	AC	3 ms; 9,948 KB
testcase_17	AC	4 ms; 9,968 KB
testcase_18	AC	145 ms; 18,944 KB
testcase_19	AC	73 ms; 14,688 KB
testcase_20	AC	16 ms; 10,508 KB
testcase_21	AC	12 ms; 12,344 KB
testcase_22	AC	8 ms; 12,144 KB
testcase_23	AC	145 ms; 20,256 KB
testcase_24	AC	16 ms; 10,552 KB
testcase_25	AC	183 ms; 22,288 KB
testcase_26	AC	192 ms; 22,592 KB
testcase_27	AC	126 ms; 20,260 KB
testcase_28	AC	2 ms; 6,816 KB
testcase_29	AC	24 ms; 12,960 KB
testcase_30	AC	57 ms; 16,280 KB
testcase_31	AC	1 ms; 6,820 KB
testcase_32	AC	1 ms; 6,816 KB
testcase_33	AC	114 ms; 18,560 KB
testcase_34	AC	2 ms; 6,820 KB
testcase_35	AC	2 ms; 6,816 KB
testcase_36	AC	1 ms; 6,820 KB
testcase_37	AC	93 ms; 17,368 KB
testcase_38	AC	44 ms; 14,232 KB
testcase_39	AC	17 ms; 10,500 KB
testcase_40	AC	91 ms; 18,344 KB
testcase_41	AC	92 ms; 19,492 KB
testcase_42	AC	121 ms; 19,428 KB
testcase_43	AC	28 ms; 13,084 KB
testcase_44	AC	30 ms; 13,520 KB
testcase_45	AC	11 ms; 10,352 KB
testcase_46	AC	13 ms; 12,612 KB
testcase_47	AC	4 ms; 10,104 KB
testcase_48	AC	29 ms; 17,240 KB
testcase_49	AC	86 ms; 20,396 KB
testcase_50	AC	40 ms; 14,868 KB
testcase_51	AC	2 ms; 6,820 KB
testcase_52	AC	55 ms; 16,424 KB
testcase_53	AC	74 ms; 17,180 KB
testcase_54	AC	42 ms; 13,740 KB
testcase_55	AC	66 ms; 19,348 KB
testcase_56	AC	18 ms; 10,612 KB
testcase_57	AC	1 ms; 6,816 KB
testcase_58	AC	266 ms; 23,900 KB
testcase_59	AC	155 ms; 23,488 KB
testcase_60	AC	197 ms; 19,940 KB
testcase_61	AC	180 ms; 23,424 KB
testcase_62	AC	201 ms; 22,292 KB
testcase_63	AC	185 ms; 23,560 KB
testcase_64	AC	207 ms; 23,832 KB
testcase_65	AC	165 ms; 19,872 KB
testcase_66	AC	266 ms; 27,280 KB
testcase_67	AC	179 ms; 22,820 KB
testcase_68	AC	36 ms; 15,440 KB
testcase_69	AC	2 ms; 6,816 KB
testcase_70	AC	3 ms; 10,080 KB

ソースコード

// Problem: No.2605 Pickup Parentheses
// Contest: yukicoder
// URL: https://yukicoder.me/problems/no/2605
// Memory Limit: 512 MB
// Time Limit: 2000 ms

#include<bits/stdc++.h>
#include<atcoder/all>
#define debug(x) cerr<<(#x)<<" "<<(x)<<endl
using mint=atcoder::modint998244353;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#define pii pair<ll,ll>
#define rep(i,a,b) for(ll i=(a);i<=(b);++i)
#define per(i,a,b) for(ll i=(a);i>=(b);--i)
using namespace std;
bool Mbe; 
ll read(){
	ll 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 write(ll x){
	if(x<0)putchar('-'),x=-x;
	if(x>9)write(x/10);
	putchar(x%10+'0');
}
const ll N=2e6+9,Mod=998244353,G=3,IG=332748118;
ll n,m,a[N],fac[N],ifac[N],r[N],cat[N];
ll pw(ll x,ll p){
	ll res=1;
	while(p){
		if(p&1)res=res*x%Mod;
		x=x*x%Mod;
		p>>=1;
	}
	return res;
}
void NTT(vector<ll>&a,ll n,ll sgn){
	rep(i,0,n-1){
		if(i<r[i])swap(a[i],a[r[i]]);
	}
	for(ll mid=1;mid<n;mid*=2){
		ll Wn=pw(sgn==1?G:IG,(Mod-1)/(mid<<1));
		for(ll R=mid<<1,j=0;j<n;j+=R){
			ll w=1;
			for(ll k=0;k<mid;k++,w=w*Wn%Mod){
				ll x=a[j+k],y=a[j+k+mid]*w%Mod;
				a[j+k]=(x+y)%Mod,a[j+k+mid]=(x-y+Mod)%Mod;
			}
		}
	}
	if(sgn==-1){
        ll inv=pw(n,Mod-2);
        rep(i,0,n-1)a[i]=a[i]*inv%Mod;
    }
}
void MUL(vector<ll>&f,vector<ll>&g,ll n,ll m){
	ll mxlen=n+m;
	ll p=1,c=0;
	while(p<=mxlen)p<<=1,c++;
	f.resize(p),g.resize(p);
	r[0]=0;
	rep(i,1,p-1)r[i]=(r[i>>1]>>1)|((i&1)<<(c-1));
	NTT(f,p,1),NTT(g,p,1);
	rep(i,0,p-1)f[i]=f[i]*g[i]%Mod;
	NTT(f,p,-1);
	f.resize(n+m-1);
}
vector<mint> work(ll l,ll r){
	if(l==r){
		vector<mint>vec(a[l]+1,0);
		vec[0]=1;
		if(a[l]%2==0)vec[a[l]]=(Mod-cat[a[l]/2])%Mod;
		else {
			vec.clear();
			vec.push_back(1);
		}
		return vec;
	}
	ll mid=(l+r)>>1;
	vector<mint>lf=work(l,mid);
	vector<mint>rg=work(mid+1,r);
	lf=atcoder::convolution(lf,rg);
	return lf;
}
bool Med;
int main(){
	cerr<<fabs(&Med-&Mbe)/1048576.0<<"MB\n";
	n=read(),m=read();
	if(n&1)return puts("0"),0;
	queue<vector<mint> >q;
	
	fac[0]=1;
	rep(i,1,n*2)fac[i]=fac[i-1]*i%Mod;
	ifac[n*2]=pw(fac[n*2],Mod-2);
	per(i,n*2-1,0)ifac[i]=ifac[i+1]*(i+1)%Mod;
	cat[0]=1;
	rep(i,1,n)cat[i]=fac[i*2]*ifac[i]%Mod*ifac[i]%Mod*pw(i+1,Mod-2)%Mod;
	if(m==0){
	  cout<<cat[n/2];
	  return 0;
	}
	rep(i,1,m){
		ll l=read(),r=read();
		a[i]=r-l+1;
		if(a[i]%2==0){
	  	vector<mint>vec(a[i]+1,0);
		  vec[0]=1;
		  vec[a[i]]=(Mod-cat[a[i]/2])%Mod;
		q.push(vec);
		}
		else {
			vector<mint>vec(1,0);
			vec[0]=1;
		q.push(vec);
		}
	}
while(q.size()>1){
		auto f=q.front();q.pop();
		auto g=q.front();q.pop();
		q.push(atcoder::convolution(f,g));
	}
	auto f=q.front();
	mint ans=0;
	rep(i,0,min((ll)f.size()-1,n)){
	  if((n-i)%2==0)ans=(ans+mint(cat[(n-i)/2])*f[i]);
	}
	write(ans.val());
	return 0;
}