Arrays and gcd

There are two integer arrays of size $N$, called $arr$ and $C$. They satisfy the following relation.

$C[0] = arr[0], \qquad C[i] = \gcd(C[i-1],\, arr[i]) \quad (1 \le i \le N-1)$

Here $\gcd(x, y)$ is the greatest common divisor of $x$ and $y$.

For example, $arr = [16, 16, 8, 16, 2]$ gives $C = [16, 16, 8, 8, 2]$.

Given the array $C$, find the number of arrays $arr$ that produce it, modulo $1000000007$ ($10^9+7$). Every element of $arr$ is an integer between $1$ and $num$.

The first line contains two integers $N$ ($1 \le N \le 10^5$) and $num$ ($1 \le num \le 10^9$), separated by a space.

The second line contains the elements of the array $C$, that is $C[0], C[1], \ldots, C[N-1]$, separated by spaces. ($1 \le C[i] \le num$)

Print the number of arrays $arr$ that satisfy the conditions, modulo $10^9+7$, on the first line.