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;

ll n, k, dp[100010], mod=1e9+7;

ll p(ll a, ll b) {
	if (b==0) return 1;
	ll ans=p(a, b/2)%mod;
	ans*=ans;
	ans%=mod;
	if (b%2==1) ans*=a;
	return ans%mod;
}

int main() {
	cin>>n>>k;
	for (int i=k; i>0; i--) {
		dp[i]=p((k/i), n);
		for (int j=2*i; j<=k; j+=i) {
			dp[i]-=dp[j];
			if (dp[i]<0) dp[i]+=mod;
		}
	}
	ll jwb=0;
	for (int i=1; i<=k; i++) {
		jwb+=(i*dp[i])%mod;
		jwb%=mod;
	}
	cout<<jwb<<endl;
}

