# | Time | Username | Problem | Language | Result | Execution time | Memory |
---|
20112 | | gs14004 | 팔찌 (kriii4_V) | C++14 | | 1000 ms | 17344 KiB |
This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <limits.h>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <algorithm>
#include <string>
#include <functional>
#include <vector>
#include <numeric>
#include <deque>
#include <utility>
#include <bitset>
#include <iostream>
using namespace std;
typedef long long lint;
typedef long double llf;
typedef pair<int, int> pi;
const int mod = 1e9 + 7;
lint ipow(lint x, lint p){
lint ret = 1, piv = x % mod;
while(p){
if(p&1) ret *= piv;
piv *= piv;
ret %= mod;
piv %= mod;
p >>= 1;
}
return ret;
}
int low[1000005], phi[1000005];
int n, k;
lint kpow[1000005];
int solve(int n, int k){
lint ret = 0;
for(int i=1; i*i<=n; i++){
if(n%i == 0){
ret += kpow[i] * phi[n/i] % mod;
if(i*i!=n) ret += kpow[n/i] * phi[i] % mod;
ret %= mod;
}
}
ret *= ipow(n, mod - 2);
ret %= mod;
return ret;
}
int main(){
cin >> n >> k;
phi[1] = 1;
for(int i=2; i<=n; i++){
for(int j=i; j<=n; j+=i){
if(!low[j]) low[j] = i;
}
phi[i] = i;
for(int j=i; j!=1; ){
int p = low[j];
while(j % p == 0){
j /= p;
}
phi[i] = (1ll * phi[i] * (p-1)) / p;
}
}
kpow[0] = 1;
for(int i=1; i<=n; i++){
kpow[i] = kpow[i-1] * k % mod;
}
lint ret = 2;
for(int i=1; i<=n; i++){
ret += solve(i, k);
ret %= mod;
if(i%2 == 0) ret += (1ll * (k+1) * kpow[i/2] % mod) * ((mod + 1) / 2) % mod;
else ret += kpow[i/2+1];
ret %= mod;
}
ret *= (mod + 1) / 2;
ret %= mod;
cout << ret;
}
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