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).

Examples

Input

3 2


Output

9


Input

3 200


Output

10813692


Input

100000 100000


Output

742202979
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int>P;
const double eps = 1e-8;
const int NINF = 0xc0c0c0c0;
const int INF  = 0x3f3f3f3f;
const ll  mod  = 1e9 + 7;
const ll  maxn = 1e6 + 5;
const int N = 1e5 + 5;

long long n,k,f[N];

ll power(ll a,ll b){return b?power(a*a%mod,b/2)*(b%2?a:1)%mod:1;}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>n>>k;
	ll ans=0;
	for(int i=k;i>=1;i--){
		f[i]=power(k/i,n);
		for(int j=2*i;j<=k;j+=i) f[i]-=f[j];
		ans=(ans+i*f[i]%mod)%mod;
	}
	cout<<(ans+mod)%mod<<'\n';
	return 0;
}