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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#203672#23. Awosile100952ms37248kbC++111.4kb2024-03-07 10:28:242024-03-07 14:18:33

answer

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define eps 1e-8
#define inf 0x3f3f3f3f
#define INF 0x3f3f3f3f3f3f3f3f
int n,mod;
#define M 3000000
int phi[3000005],p[3000005],vis[3000005];
int sumphi[3000005];
int cnt=0,inv6;
map<int,int>mp;
int qp(int x,int y){
	int ans=1;
	while(y){
		if(y&1)ans=(ll)ans*x%mod;
		y>>=1;
		x=(ll)x*x%mod;
	}
	return ans;
}
int fsum(int x){
	return (ll)x*(x+1)%mod*(x+x+1)%mod*inv6%mod;
}
int Phi(int x){
	if(x<=M)return sumphi[x];
	if(mp.find(x)!=mp.end())return mp[x];
	int ans=(ll)x*(x+1)/2%mod;
	int L=2;
	while(L<=x){
		int R=x/(x/L);
		ans=(ans-(ll)(R-L+1)*Phi(x/L))%mod;
		L=R+1;
	}
	return mp[x]=(ans+mod)%mod;
}
int main(){
	vis[1]=1,phi[1]=1;
	for(int i=2;i<=M;i++){
		if(!vis[i])p[++cnt]=i,phi[i]=i-1;
		for(int j=1;j<=cnt&&i*p[j]<=M;j++){
			vis[i*p[j]]=1;
			if(i%p[j]==0){
				phi[i*p[j]]=phi[i]*p[j];
				break;
			}
			phi[i*p[j]]=phi[i]*phi[p[j]];
		}
	}
	scanf("%d%d",&n,&mod);
	for(int i=1;i<=M;i++)sumphi[i]=(sumphi[i-1]+phi[i])%mod;
	// for(int i=1;i<=n;i++)printf("%d ",sumphi[i]);printf("\n");
	inv6=qp(6,mod-2);
	int L=1,ans=0;
	while(L<=n){
		int R=n/(n/L);
		// printf("%d %d %d\n",fsum(n/L),Phi(R),Phi(L-1));
		ans=(ans+(ll)fsum(n/L)*(Phi(R)-Phi(L-1)))%mod;
		L=R+1;
	}
	printf("%d",(ans+mod)%mod);
	return 0;
}
// quod erat demonstrandum

Details

小提示:点击横条可展开更详细的信息

Test #1:

score: 10
Accepted
time: 65ms
memory: 37196kb

input:

11 998244353

output:

651

result:

ok 1 number(s): "651"

Test #2:

score: 10
Accepted
time: 70ms
memory: 37196kb

input:

60 1000000009

output:

101457

result:

ok 1 number(s): "101457"

Test #3:

score: 10
Accepted
time: 72ms
memory: 37192kb

input:

73 998244353

output:

180007

result:

ok 1 number(s): "180007"

Test #4:

score: 10
Accepted
time: 78ms
memory: 37236kb

input:

9039240 1000000009

output:

443974844

result:

ok 1 number(s): "443974844"

Test #5:

score: 10
Accepted
time: 72ms
memory: 37236kb

input:

9196294 1000000009

output:

391130254

result:

ok 1 number(s): "391130254"

Test #6:

score: 10
Accepted
time: 70ms
memory: 37236kb

input:

9775622 1000000009

output:

764138175

result:

ok 1 number(s): "764138175"

Test #7:

score: 10
Accepted
time: 133ms
memory: 37244kb

input:

957560129 1000000007

output:

52164784

result:

ok 1 number(s): "52164784"

Test #8:

score: 10
Accepted
time: 132ms
memory: 37244kb

input:

951882222 998244353

output:

30965363

result:

ok 1 number(s): "30965363"

Test #9:

score: 10
Accepted
time: 126ms
memory: 37248kb

input:

928738646 1000000007

output:

981655745

result:

ok 1 number(s): "981655745"

Test #10:

score: 10
Accepted
time: 134ms
memory: 37244kb

input:

911039034 1000000009

output:

726376639

result:

ok 1 number(s): "726376639"

Extra Test:

score: 0
Extra Test Passed