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 = 1e9+7;
ll dp [1<<17];
ll binpow(ll a,ll b)
{
    a%=mod;
    ll res = 1;
    while(b>0)
    {
        if(b&1) res = res * a%mod;
        a = a*a%mod;
        b>>=1;
    }
    return res;
}
int main()
{
    ll n,k;
    cin>>n>>k;
    ll ans=0;
    for(int i=k;i>=1;i--)
    {
        dp[i] = binpow(k/i,n);
        for(int j = i+i ; j<=k;j+=i)
            dp[i]-=dp[j];
        ans+=i*dp[i]%mod;
    }
    cout<<ans%mod<<endl;
}
