Andrew is a very curious student who drew a circle with the center at
\((0,0)\) and an integer circumference
of \(C \geq 3\). The location of a
point on the circle is the counter-clockwise arc length from the
right-most point of the circle.

Andrew drew \(N \geq 3\) points at
integer locations. In particular, the \(i\)th point is drawn at location
\(P_i\) \((0 \le P_i \le C-1)\). It is possible for Andrew to draw multiple
points at the same location.

A good triplet is defined as a triplet \((a,b,c)\) that satisfies the following
conditions:

• \(1 \le a < b < c \le N\).

• The origin \((0,0)\) lies
  strictly inside the triangle with vertices at \(P_a\), \(P_b\), and \(P_c\). In particular, the origin is
  not on the triangle’s perimeter.

Lastly, two triplets \((a,b,c)\) and
\((a',b',c')\) are distinct
if \(a \ne a'\), \(b \ne b'\), or \(c \ne c'\).

Andrew, being a curious student, wants to know the number of distinct
good triplets. Please help him determine this number.

\(C \geq 3\)
\(N \geq 3\)
\((0 \le P_i \le C-1)\)
\(1 \le a < b < c \le N\)

Marks

The following table shows how the available 15 marks are
distributed.

The first line contains the integers \(N\) and \(C\), separated by one space.

The second line contains \(N\)
space-separated integers. The \(i\)th integer is \(P_i\) \((0 \le P_i \le C-1)\).

Output the number of distinct good triplets.

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출처 CCC 2022 Senior