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;
const ll mod = 1e9 + 7;
const int N = 1e5 + 10;

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


ll n, k;
ll cnt[N]; 

int main()
{
	scanf("%lld%lld", &n, &k);
	ll ans = 0;
//	ll cnt = 1;
	for (ll i = k; i >= 1; i --)
	{
		ll tmp = k / i;
		cnt[i] = qmi(tmp, n);
		for (ll j = i + i; j <= k; j += i)
		{
			cnt[i] = (cnt[i] - cnt[j] + mod) % mod;
		}
		ans = (ans + cnt[i] * i % mod) % mod;
	}	
	cout << ans << endl;
}