Score : $500$ points
We have a loaf of bread of length $L$, which we will cut and distribute to $N$ children.
The $i$-th child $(1\leq i\leq N)$ wants a loaf of length $A_i$.
Now, Takahashi will repeat the operation below to cut the loaf into lengths $A_1, A_2, \ldots, A_N$ for the children.
Choose a loaf of length $k$ and an integer $x$ between $1$ and $k-1$ (inclusive). Cut the loaf into two loaves of length $x$ and $k-x$.
This operation incurs a cost of $k$ regardless of the value of $x$.
Each child $i$ must receive a loaf of length exactly $A_i$, but it is allowed to leave some loaves undistributed.
Find the minimum cost needed to distribute loaves to all children.
Input is given from Standard Input in the following format:
$N$ $L$ $A_1$ $A_2$ $\ldots$ $A_N$
Print the minimum cost needed to distribute loaves to all children.
5 7 1 2 1 2 1
16
Takahashi can cut the loaf for the children as follows.
This incurs a cost of $7+3+2+4=16$, which is the minimum possible. There will be no leftover loaves.
3 1000000000000000 1000000000 1000000000 1000000000
1000005000000000
Note that each child $i$ must receive a loaf of length exactly $A_i$.