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 <iostream>
#include <cstdlib>
#include <cstdio>
using namespace std;
const int mo=1e9+7;
const int maxn=1e5+10;
int n,k;
long long dp[maxn],ans;
long long po(long long a,long long b)
{
	if (b==0) return 1;
	if (b==1) return a%mo;
	long long c=po(a,b/2);
	if (b&1) return c*c%mo*a%mo;else return c*c%mo;
}
int main()
{
	scanf("%d%d",&n,&k);
	for (int i=1;i<=k;i++) dp[i]=po(k/i,n);
	for (int i=k;i>=1;i--)
	 for (int j=2*i;j<=k;j+=i) dp[i]=(dp[i]-dp[j]+mo)%mo;
	for (int i=1;i<=k;i++) ans=(ans+dp[i]*i)%mo;
	printf("%lld\n",ans);
return 0;
}