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;
#define FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
ll N,K;
const ll MOD=1e9+7,MAX_K=1e5;
ll mpw(ll n,ll m){
	ll r=1;
	while(m){
		if(m&1){
			r*=n;
			r%=MOD;
		}
		m>>=1;
		n*=n;
		n%=MOD;
	}
	return r;
}
ll dp[MAX_K+1];
int main(){
	cin.tie(0);
	cin.sync_with_stdio(false);
	cin>>N>>K;
	for(ll i=K;i>0;i--){
		dp[i]=mpw(K/i,N);
		for(ll j=2*i;j<=K;j+=i){
			dp[i]+=MOD-dp[j];
			dp[i]%=MOD;
		}
	}
	ll ans=0;
	FOR(i,1,K+1){
		ans+=dp[i]*i;
		ans%=MOD;
	}
	cout<<ans<<endl;
}
