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 rep(i, n) for (int i = 0; i < (n); i++)
using namespace std;
typedef long long ll;
const ll mod = 1e9 + 7;

int n, k;

ll modpow(ll a, ll b) {
  ll r = 1;
  while (b) {
    if (b & 1) r = r * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return r;
}

ll dp[200005];

int main() {
  cin >> n >> k;
  ll ans = 0;
  for (int i = 1; i <= k; i++) dp[i] = modpow(k / i, n);

  for (int i = k; i > 0; --i)
    for (int j = 2; j < k / i + 1; ++j) dp[i] -= dp[i * j];

  rep(i, k + 1) ans += dp[i] * i, ans %= mod;

  cout << ans << endl;
}
