A10064 | Geometric Progression

Polycarp loves geometric progressions very much. Since he was only three years old, he loves only the progressions of length three. He also has a favorite integer $k$ and a sequence $a$ , consisting of $n$ integers.

He wants to know how many subsequences of length three can be selected from $a$ , so that they form a geometric progression with common ratio $k$ .

A subsequence of length three is a combination of three such indexes $i_{1},i_{2},i_{3}$ , that $1<=i_{1}<i_{2}<i_{3}<=n$ . That is, a subsequence of length three are such groups of three elements that are not necessarily consecutive in the sequence, but their indexes are strictly increasing.

A geometric progression with common ratio $k$ is a sequence of numbers of the form $b·k^{0},b·k^{1},...,b·k^{r-1}$ .

Polycarp is only three years old, so he can not calculate this number himself. Help him to do it.

The first line of the input contains two integers, $n$ and $k$ ( $1<=n,k<=2·10^{5}$ ), showing how many numbers Polycarp's sequence has and his favorite number.

The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $-10^{9}<=a_{i}<=10^{9}$ ) — elements of the sequence.

Output a single number — the number of ways to choose a subsequence of length three, such that it forms a geometric progression with a common ratio $k$ .