Submission #4022840


Source Code Expand

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;
 
#define fi first
#define se second
#define mp make_pair
#define pb push_back
 
typedef long long ll;
typedef pair<int,int> ii;
typedef vector<int> vi;
typedef unsigned long long ull;
typedef long double ld; 
typedef tree<ii, null_type, less<ii>, rb_tree_tag, tree_order_statistics_node_update> pbds;

struct NumberTheory
{
	vector<ll> primes;
	vector<bool> prime;
	vector<ll> totient;
	vector<ll> sumdiv;
	vector<ll> bigdiv;
	void Sieve(ll n)
	{
		prime.assign(n+1, 1);
		prime[1] = false;
		for(ll i = 2; i <= n; i++)
		{
			if(prime[i])
			{
				primes.pb(i);
				for(ll j = i*2; j <= n; j += i)
				{
					prime[j] = false;
				}
			}
		}
	}
	
	ll phi(ll x)
	{
		map<ll,ll> pf;
		ll num = 1; ll num2 = x;
		for(ll i = 0; primes[i]*primes[i] <= x; i++)
		{
			if(x%primes[i]==0)
			{
				num2/=primes[i];
				num*=(primes[i]-1);
			}
			while(x%primes[i]==0)
			{
				x/=primes[i];
				pf[primes[i]]++;
			}
		}
		if(x>1)
		{
			pf[x]++; num2/=x; num*=(x-1);
		}
		x = 1;
		num*=num2;
		return num;
	}
	
	int mobius(ll x)
	{
		int ans=1;
		for(ll i = 0; primes[i]*primes[i] <= x; i++)
		{
			int cnt=0;
			while(x%primes[i]==0)
			{
				x/=primes[i];
				cnt++;
			}
			if(cnt>=2) return 0;
			if(cnt==1) ans*=-1;
		}
		if(x>1) ans*=-1;
		return ans;
	}
};

const int MOD = (1e9 + 7);
int add(int a, int b)
{
	a+=b;
	while(a>=MOD) a-=MOD;
	return a;
}
int mult(int a, int b)
{
	return (a*1LL*b)%MOD;
}
int modpow(int a, int b)
{
	int r=1;
	while(b)
	{
		if(b&1) r=mult(r,a);
		a=mult(a,a);
		b>>=1;
	}
	return r;
}

map<int,vi> D;
map<int,int> phimap;
map<int,int> mobiusmap;	
NumberTheory nt;

int phi(int x)
{
	if(phimap.find(x)==phimap.end()) return (phimap[x]=nt.phi(x));
	return phimap[x];
}

int mobius(int x)
{
	if(mobiusmap.find(x)==mobiusmap.end()) return (mobiusmap[x]=nt.mobius(x));
	return mobiusmap[x];
}

int main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	int n,k; cin>>n>>k;
	nt.Sieve(100011);
	vector<int> divi;
	for(int d=1;d*d<=n;d++)
	{
		if(n%d==0)
		{
			divi.pb(d);
			if(d*d!=n) divi.pb(n/d);
		}
	}
	sort(divi.begin(),divi.end());
	for(int x:divi)
	{
		for(int y:divi)
		{
			if(x%y==0) D[x].pb(y);
		}
	}
	int ans = 0;
	for(int d:divi)
	{
		//minimal period = d
		int res = 0;
		for(int v:D[d])
		{
			res = add(res, mult(MOD+mobius(d/v),modpow(k,(v+1)/2)));
		}
		if(d%2==0) res=mult(res,modpow(2,MOD-2));
		res=mult(res,d);
		ans=add(ans,res);
	}
	cout<<ans<<'\n';
}

Submission Info

Submission Time
Task F - Rotated Palindromes
User zscoder
Language C++14 (GCC 5.4.1)
Score 1000
Code Size 2722 Byte
Status AC
Exec Time 36 ms
Memory 1280 KB

Judge Result

Set Name Sample All
Score / Max Score 0 / 0 1000 / 1000
Status
AC × 4
AC × 36
Set Name Test Cases
Sample 0_00.txt, 0_01.txt, 0_02.txt, 0_03.txt
All 0_00.txt, 0_01.txt, 0_02.txt, 0_03.txt, 1_00.txt, 1_01.txt, 1_02.txt, 1_03.txt, 1_04.txt, 1_05.txt, 1_06.txt, 1_07.txt, 1_08.txt, 1_09.txt, 1_10.txt, 1_11.txt, 1_12.txt, 1_13.txt, 1_14.txt, 1_15.txt, 1_16.txt, 1_17.txt, 1_18.txt, 1_19.txt, 1_20.txt, 1_21.txt, 1_22.txt, 1_23.txt, 1_24.txt, 1_25.txt, 1_26.txt, 1_27.txt, 1_28.txt, 1_29.txt, 1_30.txt, 1_31.txt
Case Name Status Exec Time Memory
0_00.txt AC 2 ms 512 KB
0_01.txt AC 2 ms 512 KB
0_02.txt AC 2 ms 512 KB
0_03.txt AC 2 ms 512 KB
1_00.txt AC 2 ms 512 KB
1_01.txt AC 2 ms 512 KB
1_02.txt AC 3 ms 512 KB
1_03.txt AC 3 ms 512 KB
1_04.txt AC 2 ms 512 KB
1_05.txt AC 2 ms 512 KB
1_06.txt AC 2 ms 512 KB
1_07.txt AC 2 ms 512 KB
1_08.txt AC 3 ms 512 KB
1_09.txt AC 3 ms 512 KB
1_10.txt AC 3 ms 512 KB
1_11.txt AC 3 ms 512 KB
1_12.txt AC 2 ms 512 KB
1_13.txt AC 2 ms 512 KB
1_14.txt AC 2 ms 512 KB
1_15.txt AC 2 ms 512 KB
1_16.txt AC 36 ms 1280 KB
1_17.txt AC 36 ms 1280 KB
1_18.txt AC 36 ms 1280 KB
1_19.txt AC 36 ms 1280 KB
1_20.txt AC 30 ms 1076 KB
1_21.txt AC 30 ms 1076 KB
1_22.txt AC 30 ms 1152 KB
1_23.txt AC 30 ms 1076 KB
1_24.txt AC 2 ms 512 KB
1_25.txt AC 2 ms 512 KB
1_26.txt AC 2 ms 512 KB
1_27.txt AC 2 ms 512 KB
1_28.txt AC 2 ms 512 KB
1_29.txt AC 2 ms 512 KB
1_30.txt AC 2 ms 512 KB
1_31.txt AC 2 ms 512 KB