Problem:
Score : 500 points

Problem Statement

Consider sequences \{A_1,...,A_N\} of length N consisting of integers between 1 and K (inclusive).

There are K^N such sequences. Find the sum of \gcd(A_1, ..., A_N) over all of them.

Since this sum can be enormous, print the value modulo (10^9+7).

Here \gcd(A_1, ..., A_N) denotes the greatest common divisor of A_1, ..., A_N.

Constraints

2 \leq N \leq 10^5

1 \leq K \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the sum of \gcd(A_1, ..., A_N) over all K^N sequences, modulo (10^9+7).

Sample Input 1

3 2

Sample Output 1

9

\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)
+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)
=1+1+1+1+1+1+1+2=9

Thus, the answer is 9.

Sample Input 2

3 200

Sample Output 2

10813692

Sample Input 3

100000 100000

Sample Output 3

742202979

Be sure to print the sum modulo (10^9+7).

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(k,i,n) for(ll i=k;i<n;++i)
const ll mod=1e9+7;
ll Pow(ll x,ll n){
    if(n==0)return 1;
    if(n%2==0)return Pow(x*x%mod,n/2)%mod;
    else return x*Pow(x%mod,n-1)%mod;
}
int main(void){
    ll n,k;
    cin>>n>>k;
    ll ans=0;
    ll tmp0[k+1];
    rep(0,i,k){
        ll d=k-i;
        ll tmp=Pow(k/d,n);
        //cout<<tmp<<endl;
        rep(2,j,k+1){
            ll nd=j*d;
            if(nd>k)break;
            else{
                tmp-=tmp0[nd];//Pow(k/nd,n);
            }
            //cout<<tmp<<endl;
        }
        tmp0[d]=tmp;
        ans+=d*tmp;
        ans%=mod;
        //cout<<ans<<endl;
    }
    ans%=mod;
    cout<<ans;
}