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>
#define ll long long
#define inf 0x3f3f3f3f
using namespace std;
const int maxn = 1e5+5;
ll mod = 1e9+7;
ll pre[maxn], pp[maxn];

ll p(ll x, ll y){
	ll res = 1;
	while(y){
		if(y & 1) res = res * x % mod;
		x = x * x % mod;
		y >>= 1;
	}
	return res % mod;
}

int main(){
	ll n, k; cin >> n >> k;
	for(ll i = 1; i <= n; i++) pp[i] = pp[i-1] + i;
	ll ans = 0, x, y;
	for(ll i = k; i >= 1; i--){
		pre[i] = p(k / i, n);
		for(int j = i*2; j <= k; j += i){
			pre[i] = (pre[i] - pre[j] + mod) % mod;
		}
		ans = (ans + pre[i] * i % mod) % mod;
	}
	cout << ans << endl;
}