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
// E - Sum of gcd of Tuples (Hard)
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define MOD 1000000007
ll modpow(ll a,ll n){return n?modpow(a*a%MOD,n/2)*(n%2?a:1)%MOD:1;}

int main(){
	int N,K; cin>>N>>K;
	vector<ll> cnt(K+1); // [gcd:[1,K]] gcd 毎の個数
	ll ans = 0;
	for(int g=K; g>=1; --g){ // g: gcd を固定
		ll c = modpow(K/g, N); // g の倍数の個数
		for(int n=2; n*g<=K; ++n) c -= cnt[n*g]; // g*1 以外を除去
		ans += c * g % MOD;
		cnt[g] = c;
	}
	cout<< ans % MOD <<endl;
}