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<memory.h>
#define mod 1000000007
#define inv(a) exp(a,mod-2)
typedef long long lld;
lld exp(lld a, lld b){
if(b==0)return 1;
lld k=exp(a, b/2);
k=(k*k)%mod;
if(b%2)k=(k*a)%mod;
return k;
}
lld fac[1001001], rfac[1001001];
void init(){
lld i;
fac[0]=rfac[0]=1;
for(i=1; i<=1000000; i++){
fac[i]=(fac[i-1]*i)%mod;
rfac[i]=inv(fac[i]);
}
}
lld comb(lld a, lld b){
return fac[a]*rfac[b]%mod*rfac[a-b]%mod;
}
lld n, k;
lld all[1001001];
lld all2[1001001];
lld sum, lr, dap;
int main(){
lld i, j;
// init();
scanf("%lld%lld", &n, &k);
all[0]=1;
for(i=1; i<=n; i++){
all[i]%=mod;
if(all[i]<0)all[i]+=mod;
all[i]+=exp(k,i), all[i]%=mod;
for(j=2*i; j<=n; j+=i)all[j]-=all[i];
}
for(i=1; i<=n; i++){
sum += all[i]*(n/i)%mod * inv(i);
sum %= mod;
}
all2[0]=1;
for(i=1; i<=n; i++){
all2[i]%=mod;
if(all2[i]<0)all2[i]+=mod;
all2[i]+=exp(k,i/2+1), all2[i]%=mod;
for(j=2*i; j<=n; j+=i)all2[j]-=all2[i];
}
all2[4]=2;
for(i=1; i<=n; i++){
lld im = all2[i]*(n/i)%mod;
if(i%2 == 0)im *= inv(2);
// else im *= inv(i);
lr += im;
lr %= mod;
}
// if(n>=2)lr += all[2]*inv(2), lr%=mod;
dap = (sum+lr)*inv(2)%mod;
dap = (dap+1)%mod;
printf("%lld", dap);
return 0;
}
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