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>
using namespace std;
typedef long long ll;

const ll MOD = 1000000007;

ll modpow(ll x, ll n){
    ll res = 1, r = x;
    while(n){
        if(n & 1) res = res * r % MOD;
        r = r * r % MOD;
        n >>= 1;
    }
    return res;
}

int main()
{
    ll n, k;
    cin >> n >> k;
    ll d[100005]{0};
    ll ans = 0;
    for(ll i = k; i >= 1; i--){
        d[i] = modpow(k / i, n);
        for(int j = i * 2; j <= k; j += i) d[i] = (d[i] + MOD - d[j]) % MOD;
        ans = (ans + d[i] * i) % MOD;
    }
    cout << ans << endl;
}
