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 int maxn=2e5+50;
const int mod=1e9+7;
ll qp(ll k,ll x){
	ll res=1;while(x){
		if(x&1) res=res*k%mod;k=k*k%mod;x>>=1;
	}return res;
}ll cnt[maxn];
int main(){
	ll n,k;scanf("%lld%lld",&n,&k);
	for(int i=1;i<=k;i++){
		cnt[i]=qp(k/i,n);
	}ll ans=0;
	for(int i=k;i>=1;i--){
		for(int j=2*i;j<=k;j+=i){
			cnt[i]=(cnt[i]-cnt[j]+mod)%mod;
		}ans+=cnt[i]*i%mod;ans%=mod;
	}printf("%lld\n",ans);
}