gabrielpeart / euler-totient-function-extended

Extended implementation of Euler Totient Function

Euler-Totient-Function-Extended

Euler totient function (denoted by phi(N)) for a positive integer N is defined as number of positive integers less than or equal N that are coprime to N.

Let's generalize this concept of Euler totient function. For positive integer N let's write out the integers that are less than or equal to N and are coprime to N. We'll get a list of integers of the form A₁, A₂, ..., A_M, where M = phi(N). Let's denote E_K(N) = A₁^K + A₂^K+...+A_M^K. This way we obtain something more general version of Euler totient function, in particular, E₀(N) = phi(N) for every positive integer N. Task is to calculate E_K(N). As answer could be large, print the answer modulo 10⁹+7

Input

The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. The first line of each test case contains two space separated integers N and K.

Output

For each test case, output a single line containing the answer to the problem i.e. the value of E_K(N) modulo 10⁹+7.

Constraints

1 ≤ T ≤ 128

Subtask 1

1 ≤ N ≤ 10^4
0 ≤ K ≤ 10^4

Subtask 2

1 ≤ N ≤ 10^12
K = 0

Subtask 3

1 ≤ N ≤ 10^12
K = 1

Subtask 4

1 ≤ N ≤ 10^12
0 ≤ K ≤ 256