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;
#define rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
constexpr int MOD = 1e9+7;
int n, k;
ll dp[100005], ans;
ll exp(ll b, ll n){
	ll res = 1;
	for(; n; n/=2,(b*=b)%=MOD) if(n%2) (res *= b) %= MOD;
	return res;
}

int main(){
	scanf("%d%d", &n, &k);
	for(int i=k; i; i--){
		dp[i] = exp(k/i,n);
		for(int j=i*2; j<=k; j+=i) (dp[i] += MOD - dp[j]) %= MOD;
		(ans += dp[i] * i) %= MOD;
	}
	printf("%lld\n", ans);
}