#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
//k^n/i-2*i-3*i-4*i-5*i-........
ll power(ll a,ll b)
{
	return b? power ( a * a % mod , b / 2 ) * ( b % 2 ? a : 1 ) % mod : 1 ;
}
int main(){
    ll n,k;
    cin>>n>>k;
    ll dp[k+1],ans=0;	
    for(ll i=k;i>=1;i--)
	{
        dp[i]=power(k/i,n);
        for(ll j=2*i;j<=k;j+=i) 
			dp[i]-=dp[j];
        ans=(ans+i*dp[i]%mod)%mod;
    }
    cout<<(ans+mod)%mod;
    return 0;
}

### Prompt

Please formulate a CPP solution to the following problem:

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

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
//k^n/i-2*i-3*i-4*i-5*i-........
ll power(ll a,ll b)
{
	return b? power ( a * a % mod , b / 2 ) * ( b % 2 ? a : 1 ) % mod : 1 ;
}
int main(){
    ll n,k;
    cin>>n>>k;
    ll dp[k+1],ans=0;	
    for(ll i=k;i>=1;i--)
	{
        dp[i]=power(k/i,n);
        for(ll j=2*i;j<=k;j+=i) 
			dp[i]-=dp[j];
        ans=(ans+i*dp[i]%mod)%mod;
    }
    cout<<(ans+mod)%mod;
    return 0;
}

```