Sensor Calliberation

Bob is organizing the inventory for an upcoming robotics bootcamp. He has a box containing \(N\) different ultrasonic sensors. Each sensor has a specific operating frequency, denoted by an integer \(A_i\).

To successfully calibrate the main control board, Bob needs to pair up the sensors. A pair of sensors \(i\) and \(j\) (where \(1 \le i < j \le N\)) is considered perfectly calibrated if the sum of their operating frequencies is exactly divisible by a target frequency \(K\).

Given the frequencies of all \(N\) sensors and the target frequency \(K\), help Bob determine the total number of perfectly calibrated pairs he can form.

Input Format

• The first line contains two space-separated integers, \(N\) and \(K\): the number of sensors and the target frequency.
• The second line contains \(N\) space-separated integers \(A_1, A_2, \dots, A_N\), representing the operating frequencies of the sensors.

Output Format

• Print a single integer: the total number of perfectly calibrated pairs.

Constraints

• \[1 \le N \le 2 \cdot 10^5\]
• \[1 \le K \le 10^5\]
• \[1 \le A_i \le 10^9\]

Sample Input 0

6 5
2 8 3 10 5 7

Sample Output 0

5