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 ll MOD=1000000007LL;
ll n,k,dp[200100],ans;
ll modp(ll a, ll b)
{
	if(b==0)return 1;
	ll u=modp(a, b/2);
	u=(u*u)%MOD;
	if(b&1)return (a*u)%MOD;
	return u;
}
int main()
{
	cin>>n>>k;
	for(ll i=k;i>=1;i--)
	{
		ll ch=k/i; ch=modp(ch, n);
		for(int j=2*i;j<=k;j+=i)
		{
			ch=(ch-dp[j]+MOD)%MOD;
		}
		dp[i]=ch;
		ch=(ch*i)%MOD;
		ans=(ans+ch)%MOD;
	
	}
	cout<<ans<<endl;
	return 0;
}
