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>
#include <vector>
using namespace std;
typedef long long ll;
ll M = 1e9 + 7;
ll mypw(ll n, ll m)
{
    if(m <= 1) return n;
    ll k = mypw(n, m/2) % M;
    k = (k*k) % M;
    if(m & 1) return (k*n)%M;
    else      return k;
}
int main()
{
    ll n, k, ans = 0;
    cin >> n >> k;
    vector<ll> c(k+1);
    for(ll i = k; i >= 1; i--) {
        c[i] = mypw(k/i, n);
        for(ll j = i*2; j <= k; j+=i) {
            c[i] -= c[j];
            if(c[i] < 0) c[i] += M;
        }
        ans = (ans + (c[i]*i)%M) % M;
    }
    cout << ans << endl;
    return 0;
}