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 int ll;

ll M = 1e9+7;
ll power(ll a , ll n)
{
    unsigned long long int result=1,x=a;
    while(n>0)
    {
        if(n % 2 ==1)
            result=(result * x)%M;
        x = (x * x)%M;
        n=n/2;
    }
    return result;
}
int main()
{
    ll n,k;
    cin >> n >> k;
    ll ans = 0;
    ll dp[k+1];   
    for(ll i=k; i>=1 ; i--)
    {
        ll ka = k/i;
        ll p = power(ka,n);
        for(ll j=2*i ; j<=k ; j=j+i)
            p = (p - dp[j] + M)%M;
        dp[i] = p;
        ans = (ans + i*p)%M;
    }
    cout << ans;
    return 0;
}