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;
typedef long long ll;


const ll mod = 1e9 + 7;


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

ll n,k;
ll ans;
ll dp[100005];

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

  for(ll i = k; i >= 1; i--) {
    dp[i] = f(k/i,n);
    for(ll j = i + i; j <= k; j += i) dp[i] -= dp[j];

    ans = (ans + ((dp[i] % mod + mod) * i % mod)) % mod;
  }

  cout << ans % mod << endl;
}
