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>

typedef long long ll;
const ll mod = 1e9 + 7;
using namespace std;

ll n, k;
ll f[100010];
ll power(ll a, ll b)
{
  return b?power(a * a % mod, b / 2) * (b % 2 ? a : 1) % mod : 1;
}
long long ans;
int main()
{
  cin >> n >> k;
  for(int i = k; i >= 1; i--)
  {
		f[i] = power(k/i, n);
    for(int j = 2*i; j <= k; j+=i)
    {
		f[i] -= f[j];
    }
    ans = (ans + i * f[i] % mod) % mod;
  }
  cout << (ans + mod) % mod << endl;
	return 0;
}