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>
using namespace std;
using ll = long long;
constexpr ll MOD = 1000000007;

ll n, k, c, a[200010];

ll modpow(ll x, ll e) {
  ll res = 1;
  while (e > 0) {
    if (e & 1) res = res * x % MOD;
    x = x * x % MOD;
    e >>= 1;
  }
  return res;
}


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

  ll ans = k;
  a[k] = 1;
  for (ll i = k - 1; i > 0; --i) {
    a[i] = modpow(k / i, n);
    for (ll j = i * 2; j <= k; j += i) {
      a[i] = (a[i] - a[j] + MOD) % MOD;
    }
    ans = (ans + a[i] * i % MOD) % MOD;
  }
  cout << ans;
  return 0;
}

