Problem Description

In a plane, there is a circle with center coordinates (0,0) and circumference C.

There are C integer points on the circumference, numbered 0 to C-1.

Among them:

• Point 0: the rightmost point on the circle
• Points 1 to C-1: the counterclockwise arc length from point 0 to the point itself exactly equals its own number

Given an integer sequence P₁, P₂, ..., P_N of length N (where 0 ≤ P_i ≤ C-1).

Please calculate how many distinct integer triples (a, b, c) simultaneously satisfy:

1. 1 ≤ a < b < c ≤ N
2. The origin (0,0) is strictly inside the triangle with vertices at points P_a, P_b, P_c
   (Note: points on the edges of the triangle are not considered inside)

Input Format

• First line: two integers N, C
• Second line: N integers P₁, P₂, ..., P_N

Output Format

One integer representing the number of triples that satisfy the conditions.

Constraints

• 3 ≤ N ≤ 10⁶
• 3 ≤ C ≤ 10⁶
• 0 ≤ P_i ≤ C-1
• Note: The P_i are not necessarily distinct

Example

Input:

8 10
0 2 5 5 6 9 0 0

Output:

6

Explanation:

The triples that satisfy the condition are:
(1,2,5), (2,3,6), (2,4,6), (2,5,6), (2,5,7), (2,5,8)