Minimum Shelves Required

You are given N books and a shelf with a maximum capacity C. Each book i occupies a certain space given by a_i. Your task is to compute the minimum number of shelves required to store all the books if you can place books on a shelf as long as the total space occupied does not exceed the shelf capacity C.

Note: You are allowed to arrange the books in any order. One possible strategy is to sort the books in descending order and then use a greedy algorithm to allocate books to shelves. Mathematically, you are to minimize the number of shelves S such that:

\[ \sum_{i \in S_j} a_i \leq C,\quad \text{for every shelf } S_j,\ j=1,2,\ldots,S \]

It is guaranteed that each book's size is a positive integer and that a valid arrangement always exists.

inputFormat

The input is read from stdin and has the following format:

• The first line contains two space-separated integers: N (the number of books) and C (the capacity of each shelf).
• The second line contains N space-separated integers: a1, a2, ..., aN, where ai is the space taken by the i-th book.

outputFormat

Output a single integer to stdout — the minimum number of shelves required to store all the books.

## sample

5 10
2 3 8 9 3

3

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