Domo is a brilliant dog. During Domo's exploration on the waterway, he discovered a treasure. Unfortunately, he doesn't know the password for the treasure chest yet. Please help him find the password so he can claim the treasure.
On the treasure chest, there is a sequence of numbers, and the password for the treasure chest is the count of subsequences that follow the rules below:
1. The length of the subsequence is 4.
2. The sum of the subsequence is S.
3. The subsequnce [Ai, Aj, Ak, Al] should satisfies that Ai ≤ Aj ≤ Ak ≤ Al
For example, if the sequence is [1, 1, 1, 3, 3, 5, 1], and S is 8
Then, the following four subsequences satisfy the rules above.
1. [1, 1, 1, 5], where the index is 0, 1, 2, 5
2. [1, 1, 3, 3], where the index is 0, 1, 3, 4
3. [1, 1, 3, 3], where the index is 0, 2, 3, 4
4. [1, 1, 3, 3], where the index is 1, 2, 3, 4
Hence, the password would be 4.
The first line consists of two integers N (1 ≤ N ≤ 50) and S (1 ≤ S ≤ 100), describing the length of the sequence and S.
The next line consists of N integers, describing the given sequence. (0 ≤ Ai ≤ 50)
Output the password of the chest. Remember to print a newline character at the end of the line.