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>
#define mod 1000000007
using namespace std;
inline long long ksm(long long x,long long y)
{
	long long rtn=1;
	while(y)
	{
		if(y&1) rtn*=x,rtn%=mod;
		x*=x,x%=mod,y>>=1;
	}
	return rtn;
}
long long cnt[100005];
int main(int argc, char** argv) {
	long long n,k,ans=0;
	cin >> n >> k;
	for(long long i=k;i>=1;i--)
	{
		cnt[i]=ksm(k/i,n);
		for(long long j=i+i;j<=k;j+=i)
			cnt[i]-=cnt[j],cnt[i]%=mod;
		cnt[i]+=mod,cnt[i]%=mod;
		ans+=cnt[i]*i%mod,ans%=mod;
	}
	cout << ans;
	return 0;
}