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 <cstdio>

using namespace std;

typedef long long ll;

const ll M = 1000000007;
ll n, k;
ll d[100005];
ll ans;

ll f(ll p, ll q)
{
    if(q == 0) return 1;
    ll t = f(p, q / 2);
    if(q % 2 == 0) return t * t % M;
    else return t * t % M * p % M;
}

int main()
{
    scanf("%lld%lld", &n, &k);
    for(ll i = 1; i <= k; i++)
    {
        ll t = (d[i] + i) % M;
        ll t2 = f(k / i, n);
        ans += t * t2 % M;
        ans %= M;
        for(ll j = i * 2; j <= k; j += i) d[j] += M - i - d[i], d[j] %= M;
    }
    cout<<ans<<endl;
    return 0;
}
