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 int long long
#define mod 1000000007

using namespace std;

int raise(int number, int exponent) {
    int answer = 1;
    while (exponent) {
        if (exponent & 1) {
            answer = answer * number % mod;
        }
        number = number * number % mod;
        exponent >>= 1;
    }
    return answer;
}

int a[200010];

int32_t main()
{
	int n,k;
	cin >> n >> k;

	int ans = 0;

	for(int i=k;i>=1;i--)
	{
		a[i] = raise(k/i, n);

		for(int j=2*i;j<=k;j+=i)
			a[i] = (a[i] - a[j] + mod)%mod;

		ans = (ans + i*a[i])%mod;
	}

	cout << ans << endl;
}