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;
#define f(i,a,b) for(register int i = a;i <= b; ++i)
const int N = 2e5+5, mod=1e9+7;
ll n,k,pri[N],g[N],s[N];
bool is[N];ll ans;
ll qpow(ll a,int b) {
	ll c=1;
	while(b) {
		if(b&1) c=c*a%mod;
		a=a*a%mod;
		b>>=1;
	} return c;
}
int main() {
	scanf("%d%d",&n,&k);
	f(i,1,k) s[i]=i-1;
	s[1]=1;
	f(i,2,k) for(int j=i+i;j<=k;j+=i)  s[j]-=s[i];
	f(i,1,k) (ans+=qpow(1ll*k/i,n)*s[i])%=mod;
	printf("%lld",ans);
}