Counting Necklaces.cpp

#include<bits/stdc++.h>
using namespace std;
#define INF 2047483647
#define INFL 9223372036854775807
#define ll long long int
#define pii pair<ll,ll>
#define F first
#define S second
#define mp make_pair
#define pb push_back
#define ull unsigned long long
#define M 1000000007
#define FASTIO ios_base::sync_with_stdio(false);cin.tie(NULL); cout.tie(NULL);
#define take(x) scanf("%d",&x)
#define DE(x) printf("\ndebug %d\n",x);
#define vout(x) for(int i=0;i<x.size();i++) printf("%d ",x[i]);
#define pie acos(-1)
#define MOD 998244353


int Set(int N,int pos){return N=N | (1<<pos);}
int reset(int N,int pos){return N= N & ~(1<<pos);}
bool check(int N,int pos){return (bool)(N & (1<<pos));}

long long bigmod(long long a, long long b, long long m=M) {
    a %= m;
    long long res = 1;
    while (b > 0) {
        if (b & 1)
            res = (res * a) % m;
        a = (a * a) % m;
        b >>= 1;
    }
    return res;
}


int main(){
    int n,m;
    cin>>n>>m;
    ll res = 0;
    for(int i=0;i<n;i++){
        res+= bigmod(m,__gcd(i,n));
        res%=M;
    }
    res = res*bigmod(n,M-2);
    res%=M;
    cout<<res;
}