D. Take5
time limit per test
2 seconds
memory limit per test
6 megabytes
input
standard input
output
standard output

Pay attention to the memory limit for this problem!

You are given an array A of size N and a positive integer S. You need to find the number of ways W in which you can chose 5 elements with distinct positions such that their sum is equal to S.

Input

The first line contains two positive integer N,  S (1 ≤ N ≤ 103,  0 ≤ S ≤ 2 * 109) - the size of the array and the queried sum.

The next line contains N numbers Ai (0 ≤ Ai ≤ 4 * 108,  1 ≤ i ≤ N).

Output

Print the only integer W (0 ≤ W < 231) - the number of ways to chose the elements.

Example
Input
6 5
1 1 1 1 1 1
Output
6