\(5^{th}\) round, March \(17^{th}\), 2012

Lumberjack Mirko needs to chop down M metres of wood. It is an easy job for him since he has a nifty
new woodcutting machine that can take down forests like wildfire. However, Mirko is only allowed to
cut a single row of trees.
Mirko‟s machine works as follows: Mirko sets a height parameter H (in metres), and the machine raises
a giant sawblade to that height and cuts off all tree parts higher than H (of course, trees not higher than
H meters remain intact). Mirko then takes the parts that were cut off. For example, if the tree row
contains trees with heights of 20, 15, 10, and 17 metres, and Mirko raises his sawblade to 15 metres, the
remaining tree heights after cutting will be 15, 15, 10, and 15 metres, respectively, while Mirko will take
5 metres off the first tree and 2 metres off the fourth tree (7 metres of wood in total).
Mirko is ecologically minded, so he doesn‟t want to cut off more wood than necessary. That‟s why he
wants to set his sawblade as high as possible. Help Mirko find the maximum integer height of the
sawblade that still allows him to cut off at least M metres of wood.

The first line of input contains two spa\(ce-se\)parated positive integers, N (the number of trees, \(1 \le N\) ≤
1 000 000) and M (Mirko‟s required wood amount, \(1 \le M \le 2\,000\,000\,000\)).
The second line of input contains N spa\(ce-se\)parated positive integers less than 1 000 000 000, the
heights of each tree (in metres). The sum of all heights will exceed M, thus Mirko will always be able to
obtain the required amount of wood.

The first and only line of output must contain the required height setting.

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출처 COCI 2011/2012 Contest 5