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 <iostream>
using namespace std;

typedef long long ll;

ll mod = 1e9 + 7;
ll num[100005];

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

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);
	ll n,k;
	cin >> n >> k;
	ll ans = 0;
	for (int i = k; i >= 1; i--)
	{
		int t = k / i;
		num[i] = q_pow(t,n);
		for (int j = 2; j * i <= k; j++)
		{
			num[i] = ( num[i] - num[i*j] + mod ) % mod;
		}
		ans += ( num[i] * i ) % mod;
		ans %= mod;
	}
	cout << ans << '\n';
	return 0;
}
