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>
#define ll long long
#define MOD 1000000007
using namespace std;
const int MAXK = 1e5 + 5;
ll f[MAXK], n, k;

ll pow(ll a, ll n)
{
    ll ans = 1;
    while (n)
    {
        if (n & 1) ans = (ans * a) % MOD;
        n >>= 1;
        a = a * a % MOD;
    }
    return ans;
}

int main()
{
    cin >> n >> k;
    
    ll ans = 0;
    for (int i = k; i >= 1; i--)
    {
        f[i] = pow(k / i, n);
        for (int j = 2 * i; j <= k; j += i)
            f[i] = (f[i] - f[j] + MOD) % MOD;
    }

    for (int i = 1; i <= k; i++) ans = (ans + i * f[i]) % MOD;
    cout << ans << endl;
}