#include<cstdio>
#include<bitset>
typedef long long ll;
ll M=int(1e9)+7;
ll pow(ll x,ll y){
if(y==0)return 1;
if(y==1)return x;
ll o=pow(x,y/2);
if(y%2==0)return o*o%M;
else return o*o%M*x%M;
}
ll ans [1000010];
ll phi [1000010];
ll kpow[1000010];
std::bitset<1000010> sieve;
int n,k;
int main(){
scanf("%d%d",&n,&k);
int i,j;
kpow[0]=1; kpow[1]=k; phi[1]=1;
for(i=2; i<=n; ++i){
kpow[i]=kpow[i-1]*k%M;
if(sieve[i]) continue;
// i is prime.
for(j=i; j<=n; j+=i){
sieve[j]=true;
if(phi[j]==0) phi[j]=j;
phi[j] /= i;
phi[j] *= i-1;
}
}
for(i=1; i<=n; ++i){
for(j=i; j<=n; j+=i){
ans[j] += phi[i] * kpow[j/i];
ans[j] %= M;
}
}
ll tmp, half=pow(2, M-2), sumans = 1;
for(i=1; i<=n; ++i){
tmp = ans[i] * half % M * pow(i,M-2) % M;
sumans += tmp;
sumans %= M;
if(i&1){
sumans += pow(k,(i+1)/2)*half%M;
sumans %= M;
} else {
sumans += (k+1)*half%M*half%M*pow(k,i/2)%M;
sumans %= M;
}
}
printf("%lld\n",sumans);
return 0;
}
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
0 ms |
24644 KB |
Output is correct |
2 |
Correct |
0 ms |
24644 KB |
Output is correct |
3 |
Correct |
0 ms |
24644 KB |
Output is correct |
4 |
Correct |
0 ms |
24644 KB |
Output is correct |
5 |
Correct |
0 ms |
24644 KB |
Output is correct |
6 |
Correct |
0 ms |
24644 KB |
Output is correct |
7 |
Correct |
0 ms |
24644 KB |
Output is correct |
8 |
Correct |
0 ms |
24644 KB |
Output is correct |
9 |
Correct |
0 ms |
24644 KB |
Output is correct |
10 |
Correct |
0 ms |
24644 KB |
Output is correct |
11 |
Correct |
0 ms |
24644 KB |
Output is correct |
12 |
Correct |
0 ms |
24644 KB |
Output is correct |
13 |
Correct |
0 ms |
24644 KB |
Output is correct |
14 |
Correct |
0 ms |
24644 KB |
Output is correct |
15 |
Correct |
0 ms |
24644 KB |
Output is correct |
16 |
Correct |
0 ms |
24644 KB |
Output is correct |
17 |
Correct |
0 ms |
24644 KB |
Output is correct |
18 |
Correct |
0 ms |
24644 KB |
Output is correct |
19 |
Correct |
0 ms |
24644 KB |
Output is correct |
20 |
Correct |
0 ms |
24644 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
0 ms |
24644 KB |
Output is correct |
2 |
Correct |
0 ms |
24644 KB |
Output is correct |
3 |
Correct |
2 ms |
24644 KB |
Output is correct |
4 |
Correct |
99 ms |
24644 KB |
Output is correct |
5 |
Execution timed out |
1000 ms |
24644 KB |
Program timed out |
6 |
Halted |
0 ms |
0 KB |
- |