Bookshelf

Farmer John recently bought a bookshelf for the cow library, but the shelf fills up quickly, and now the only free space left is at the very top.

There are $N$ cows ($1 \le N \le 20000$), and each cow $i$ has a height $H_i$ ($1 \le H_i \le 10000$). Let $S$ be the sum of all cow heights. The bookshelf has a height of $B$ ($1 \le B \le S < 2000000007$).

To reach the top of the bookshelf, which is taller than the tallest cow, one or more cows can stand on top of each other in a stack. The total height of a stack equals the sum of the individual heights of its cows, and this total must be at least the bookshelf height $B$. Because stacking more cows than necessary is dangerous, find the smallest number of cows in a stack that still reaches the bookshelf.

• Line 1: Two space-separated integers, $N$ and $B$
• Lines 2 to $N+1$: Line $i+1$ contains a single integer $H_i$.

• Line 1: A single integer, the size of the smallest set of cows that can reach the bookshelf.

For example, when the bookshelf height is $40$, one way to reach it with $3$ cows is $18+11+13$; many other ways exist.