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 <iostream>

using namespace std;
typedef long long ll;
const int N=1e5+10;
const int mod=1e9+7;
int qmi(int a,int b)
{
    int ans=1;
    while(b){
        if(b&1)ans=(ll)ans*a%mod;
        a=(ll)a*a%mod;
        b>>=1;
    }return ans;
}
ll f[N];
int main()
{
    int n,m;
    cin>>m>>n;
    for(int i=n;i>=1;i--)
    {
        ll sum=0;
        int h=n/i;
        sum=qmi(h,m);
        for(int j=i;j<=n;j+=i)
        {
            sum-=f[j];
        }
        f[i]=sum;
    }
    ll ans=0;
    for(int i=1;i<=n;i++)
    {
        ans=(ans+(ll)f[i]*i%mod)%mod;
    }
    cout<<ans<<endl;
}