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 MOD=1e9+7;
const int MAXN=1e5+5;
int n,k;
ll ans[MAXN],sum;
ll qpow(int a, int b) {
	ll ans = 1, base = a;
	while (b) {
		if (b & 1) ans = ans * base % MOD;
		b >>= 1, base = base * base % MOD;
	}
	return ans;
}
int main() {
	cin>>n>>k;
	for(int x=k; x; x--) {
		ans[x]=qpow(k/x,n);
		for(int j=2; j*x<=k; j++)
			(ans[x]-=ans[j*x])%=MOD;
		sum=sum+x*ans[x]%MOD;
	}
	cout<<(sum+MOD)%MOD;
	return 0;
}