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;
#define rep(i,a,b) for(ll i=a;i<b;i++)
#define per(i,a,b) for(ll i=b-1;i>=a;i--)
const ll maxn=1e5+5, mod=1e9+7;
ll n,k,ans[maxn],sol;
ll binpow(ll b, ll e) {
    ll ans=1;
    for(b%=mod;e;b=b*b%mod,e/=2) if(e&1) ans=ans*b%mod;
    return ans;
}
int main() {
    cin.tie(0);
    ios_base::sync_with_stdio(0);
    cin>>n>>k;
    rep(i,1,k+1) ans[i]=binpow(k/i,n);
    per(i,1,k+1)
        for(ll j=2*i;j<k+1;j+=i)
            ans[i]=(ans[i]-ans[j]+mod)%mod;
    rep(i,1,k+1) sol=(sol+ans[i]*i)%mod;
    cout<<sol<<"\n";
}
