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)

//#pragma GCC optimize(2) 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pb push_back
#define clr(a,b) memset(a,b,sizeof(a))
ll n,m,k,ans;
ll f[100005];
ll mod=1000000007;
ll pow1(ll x,ll y){
	ll a=1,b=x;while(y){if(y&1)a=(a*b)%mod;b=(b*b)%mod;y>>=1;}
	return a;
}
int main(){
	//freopen("P1429_6.in","r",stdin);
	//freopen("match.out","w",stdout);
    ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>n>>k;
	for(ll i=k;i>=1;i--){
		f[i]=pow1(k/i,n);
		for(int j=2;i*j<=k;j++){
			f[i]-=f[i*j];
		}
		ans=(ans+i*f[i])%mod;
	}
	cout<<ans;
    return 0;
}