Submission #19851

#TimeUsernameProblemLanguageResultExecution timeMemory
19851tonyjjw팔찌 (kriii4_V)C++14
100 / 100
663 ms54220 KiB
//*
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <time.h>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <numeric>
#include <functional>
#define MOD 1000000007
#define MAX 0x3f3f3f3f
#define MAX2 0x3f3f3f3f3f3f3f3fll
#define ERR 1e-10
#define mp make_pair
#define all(x) (x).begin(), (x).end()
#pragma warning(disable:4996)
using namespace std;

typedef long long ll;
typedef long double ldb;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;

int n, m;
ll pi[1040000];
ll powm[1040000];
int comp[1040000];
ll xans[1040000];
ll inv[2040000];
ll xsum[1040000];

ll mul_inv(ll a, ll b=MOD)
{
	ll b0=b, t, q;
	ll x0=0, x1=1;
	if(b == 1) return 1;
	while(a > 1)
	{
		q=a/b;
		t=b, b=a%b, a=t;
		t=x0, x0=x1-q*x0, x1=t;
	}
	if(x1 < 0) x1+=b0;
	return x1;
}


ll modpow(ll x, ll y)
{
	ll ans=1;
	while(y)
	{
		if(y%2) ans*=x, ans%=MOD;
		x*=x, x%=MOD, y/=2;
	}
	return ans;
}

int main()
{
	int i, j, k;
	cin>>n>>m;
	//int t=clock();
	for(i=1;i<=n;i++) pi[i]=i;
	powm[0]=1;
	for(i=1;i<=n;i++) powm[i]=powm[i-1]*m, powm[i]%=MOD;
	for(i=1;i<=n*2;i++) inv[i]=mul_inv(i);
	ll ans=0;
	for(i=1;i<=n;i++)
	{
		xsum[i]=powm[i]*inv[i]%MOD;
	}
	for(i=1;i<=n;i++) xsum[i]+=xsum[i-1], xsum[i]%=MOD;
	for(i=1;i<=n;i++)
	{
		ll u=0;
		int k=1;
		for(j=i;j<=n;j+=i)
		{
			if(j != i && i >= 2) comp[j]=1;
			if(i >= 2 && !comp[i])
			{
				pi[j]/=i, pi[j]*=i-1;
			}
			//u+=powm[k++]*inv[j*2]%MOD;
		}
		u+=xsum[n/i]*inv[2*i]%MOD;
		//u%=MOD;
		ans+=pi[i]*u%MOD;
	}
	ans%=MOD;
	for(i=1;i<=n;i++)
	{
		if(i%2 == 0)
		{
			ans+=inv[4]*(m+1)%MOD*powm[i/2]%MOD;
		}
		else
		{
			ans+=inv[2]*powm[(i+1)/2]%MOD;
		}
	}
	ans++;
	ans%=MOD;
	cout<<ans;
	return 0;
}
//*/
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