Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3 2

Sample Output 1

9

\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)
+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)
=1+1+1+1+1+1+1+2=9

Thus, the answer is 9.

Sample Input 2

3 200

Sample Output 2

10813692

Sample Input 3

100000 100000

Sample Output 3

742202979

Be sure to print the sum modulo (10^9+7).

Solution in C++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

typedef long long ll;
ll MOD = 1000000007;


ll my_pow(ll b, ll e) {
    if (e == 1) return b % MOD;
    if (e % 2 == 1){
        ll r = my_pow(b, (e-1) / 2);
        r = (r * r) % MOD;
        return (r * b) % MOD;
    } else {
        ll r = my_pow(b, e / 2);
        r = (r * r) % MOD;
        return r;
    }
}

int main() {
    int K, N;
    cin >> N >> K;

    ll result = 0;
    // n = K
    vector<ll> cof(K+10);
    for (int n = K; n >= 1; n--) {
        cof[n] = my_pow(floor(K / n), N);
        for (int i = n*2; i <= K; i+=n) {
            cof[n] -= cof[i];
        }
        // cout << n << " " << cof << endl;
        result = (result + cof[n] * n) % MOD;
    }

    cout << result;
}