EKO  Eko
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.
Input
The first line of input contains two spaceseparated positive integers, N (the number of trees, 1 ≤ N ≤ 1 000 000) and M (Mirko‟s required wood amount, 1 ≤ M ≤ 2 000 000 000).
The second line of input contains N spaceseparated 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.
Output
The first and only line of output must contain the required height setting.
Example
Input: 4 7 20 15 10 17 Output: 15
Input: 5 20 4 42 40 26 46 Output: 36
hide comments
yash_18:
20160604 08:53:02
used java TLE!!


aloochaat1998:
20160522 08:20:30
Anybody who doesn't have a approach,refer this:


minhthai:
20160123 15:36:23
nlogn and tle, what to do :(( 

senshiya:
20160123 11:13:27
plz provide some test cases i m getting wrong ans.... 

waelalgaml:
20151203 21:44:14
getting tle in test case 8 _ 

vedang:
20151130 14:16:47
My 150th :')


harry30:
20151129 09:19:03
is there a clue how to produce output 36 on second sample test case ? 

jkelava6:
20151023 21:02:20
I think that time limit is too strict for Python, if you are using the solution that is meant to be used on this problem!


maverick_10:
20150916 22:34:45
It's a very good and basic problem for implementing binary search I think . 

monkz:
20150903 20:00:24
does nlogn solution work??

Added by:  ghorvat 
Date:  20120702 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  COCI 2011/2012 