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;
const int maxn=2e5+50;
ll t,n,m,k;
ll rec[maxn];
const int mod=1e9+7;
ll qk(ll a,ll b,ll p)
{
	ll ans=1%p;
	while(b)
	{
		if(b&1) ans=(ans*a)%p;
		a=(a*a)%p;
		b=b>>1;
	}
	return ans;
}
int main()
{
	ios::sync_with_stdio(false);
	cin>>n>>k;
	ll fin=0;
	for(ll i=k;i>=1;i--)
	{
		ll z=k/i;
		ll zz=qk(z,n,mod);
		zz=zz%mod;
		rec[i]=zz;
		for(ll j=2;;j++)
		{
			ll zzz=i*j;
			if(zzz>k) break;
			rec[i]=(rec[i]-rec[zzz]+mod)%mod;
		}
	}
	for(int i=1;i<=k;i++)
	{
		fin=(fin+(i*rec[i])%mod)%mod;
	}
	cout<<fin<<endl;
	return 0;
}