GCD of Sequence

Alice is playing a game with Bob.
Alice shows N integers a₁, a₂, …, a_N, and M, K. She says each integers 1 ≤ a_i ≤ M.
And now Alice wants to ask for each d = 1 to M, how many different sequences b₁, b₂, …, b_N. which satisfies :
1. For each i = 1…N, 1 ≤ b[i] ≤ M
2. gcd(b₁, b₂, …, b_N) = d
3. There will be exactly K position i that ai != bi (1 ≤ i ≤ n)

Alice thinks that the answer will be too large. In order not to annoy Bob, she only wants to know the answer modulo 1000000007.Bob can not solve the problem. Now he asks you for HELP!
Notes: gcd(x₁, x₂, …, x_n) is the greatest common divisor of x₁, x₂, …, x_n

The input contains several test cases, terminated by EOF.
The first line of each test contains three integers N, M, K. (1 ≤ N, M ≤ 300000, 1 ≤ K ≤ N)
The second line contains N integers: a₁, a₂, ..., a_n (1 ≤ a_i ≤ M) which is original sequence.

For each test contains 1 lines :
The line contains M integer, the i-th integer is the answer shows above when d is the i-th number.

3 3 3
3 3 3
3 5 3
1 2 3

7 1 0
59 3 0 1 1

In the first test case :
when d = 1, {b} can be :
(1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 2, 2)
(2, 1, 1)
(2, 1, 2)
(2, 2, 1)
when d = 2, {b} can be :
(2, 2, 2)
And because {b} must have exactly K number(s) different from {a}, so {b} can't be (3, 3, 3), so Answer = 0

2013 Multi-University Training Contest 7