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;

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

int main() {
  int N, K, M = 1e9 + 7;
  cin >> N >> K;
  long ans = 0;
  vector<long> DP(K + 1);
  for (int i = K; i >= 1; i--) {
    DP.at(i) = modpow(K / i, N, M);
    for (int j = i + i; j <= K; j += i) DP.at(i) -= DP.at(j);
    ans += i * DP.at(i) % M;
  }
  cout << ans % M << "\n";
}