Good Triplets

문제

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

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Andrew drew N ≥ 3 points at integer locations. In particular, the i^th point is drawn at location P_i (0 ≤ P_i ≤ 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 ≤ a < b < c ≤ 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 ≠ a', b ≠ b', or c ≠ c'.

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

입력

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 ≤ P_i ≤ C − 1).

출력

Output the number of distinct good triplets.