bzoj4833

$数论$

$这个题已经忘了怎么做了，也不想知道了，只记得看了3个小时$

$对于有gcd(f_i, f_j) = f_{gcd(i, j)}性质的数列，以下结论适用$

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1e6 + ;
int n;
ll ans = , P;
ll f[N], g[N];
int m[N];
int rd()
{
    int x = , f = ;
    char c = getchar();
    while(c < '' || c > '') { if(c == '-') f = -; c = getchar(); }
    while(c >= '' && c <= '') { x = x *  + c - ''; c = getchar(); }
    return x * f;
}
ll power(ll x, ll t)
{
    ll ret = ;
    for(; t; t >>= , x = x * x % P) if(t & ) ret = ret * x % P;
    return ret;
}
ll inv(ll x)
{
    return power(x, P - );
}
int main()
{
    int T = rd();
    while(T--)
    {
        n = rd();
        P = rd();
        f[] = ;
        f[] = ;
        for(int i = ; i <= n; ++i) f[i] = (f[i - ] *  + f[i - ]) % P;
        for(int i = ; i <= n; ++i) g[i] = f[i];
        for(int i = ; i <= n; ++i)
        {
            ll t = inv(g[i]);
            for(int j = i + i; j <= n    ; j += i)
                g[j] = g[j] * t % P;
        }
        ll lcm = ;
        ans = ;
        for(int i = ; i <= n; ++i)
        {
            lcm = lcm * g[i] % P;
            ans = (ans + 1LL * lcm * i) % P;
        }
        printf("%lld\n", ans);
    }
    return ;
}