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>
using namespace std;
#define rep(i, a) for(int i=0; i<(a); i++)
typedef long long ll;
const ll mod = 1000000007;

ll modpow(ll a, ll n)
{
  ll res=1;
  while (n>0) {
    if (n&1) res = res*a % mod;
    a = a*a % mod;
    n >>= 1;
  }
  return res;
}

int main()
{
  ll N, K; cin >> N >> K;

  vector<ll> d(K+1);
  for (int i=K; i>=1; i--) {
    ll tmp = modpow(K/i, N);
    for (int j=2; j*i<=K; j++) {
      tmp = (tmp + mod - d[j*i]) % mod;
    }
    d[i] = tmp;
  }

  ll ans = 0;
  for (int i=1; i<=K; i++) {
    ans = (ans + i*d[i]) % mod;
  }
  cout << ans << endl;

  return 0;
}
