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; 
using ll = long long;
ll MOD = 1e9+7;

ll binpow(ll a, ll b){
	ll res = 1;
	while(b){
		if(b&1)
			res = (res * a) % MOD;
		a = (a * a) % MOD;
		b >>= 1;
	}
	return res;
}


signed main() { 
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	int n, k; 
	cin>>n>>k;
	ll sum = 0;
	map<ll, ll> m;
	for(int i = k; i >= 1; i--){
		ll cnt = 1;
		ll succ = 0;
		for(int j = 2; j*i <= k; j++){
			cnt++;
			succ += m[i*j];
		}

		ll num = ((binpow(cnt, n) - succ) % MOD + MOD) % MOD;
		m[ll(i)] = num;
		sum = (sum + (num * i) % MOD) % MOD;
	}
	cout << sum;
}
