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;
typedef long long ll;

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

int main(){
  ll N,K;
  ll mod = 1e9+7;
  cin >> N >> K;
  map<ll,ll> cnt_gcd{};
  cnt_gcd = {};
  ll ans = 0;
  cnt_gcd[K] = 1;
  for(ll i=K-1;i>=1;--i){
    cnt_gcd[i] = quickmodpow(ll(K/i),N,mod);
    for(ll j=2*i;j<=K;j=j+i){
      if(cnt_gcd[j]>=1) cnt_gcd[i] = (cnt_gcd[i] - cnt_gcd[j] + mod)%mod;
    }
  }
  for(ll i=1;i<=K;++i){
    ans = (ans + (cnt_gcd[i] * i)) % mod;
  }
  cout << ans << endl;
}