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 PyPy3 (7.3.0) (judge verdict: Accepted)

def main():
    N, K = map(int, input().split())
    MOD = 10 ** 9 + 7
    ans = 0
    cont = [0] * (K + 1)
    for i in range(K, 0, -1):
        tmp = K // i
        if tmp == 1:
            cont[i] = 1
        else:
            cont[i] = pow(tmp, N, MOD)
            for k in range(2,100000):
                if i * k > K:
                    break
                cont[i] -= cont[i*k]
                cont[i] %= MOD

    for i in range(1,K+1):
        ans += i * cont[i]
        ans %= MOD

    if sum(cont) % MOD != pow(K,N,MOD):
        ans -= sum(cont) % MOD - pow(K,N,MOD)

    print(ans)


if __name__ == "__main__":
    main()