HOTELS - Hotels Along the Croatian Coast

There are N hotels along the beautiful Adriatic coast. Each hotel has its value in Euros.

Sroljo has won M Euros on the lottery. Now he wants to buy a sequence of consecutive hotels, such that the sum of the values of these consecutive hotels is as great as possible - but not greater than M.

You are to calculate this greatest possible total value.

Input

In the first line of the input there are integers N and M (1 ≤ N ≤ 300 000, 1 ≤ M < 231).

In the next line there are N natural numbers less than 106, representing the hotel values in the order they lie along the coast.

Output

Print the required number (it will be greater than 0 in all of the test data).

Example

input
5 12
2 1 3 4 5
output
12
input
4 9
7 3 5 6
output
8

Added by:Adrian Satja Kurdija
Date:2011-10-30
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:that would be me

hide comments
2015-06-05 05:58:41 ---@@@----
Nice question..
Done it using Sliding Window concept... :)
2015-05-20 17:51:17 sathya_dev
Learnt new way of thinking :)
2015-05-19 20:03:45 Vaporeon
My dp solution giving WA ar running judge(7)..
My submission id is:14282110
please help :(
2015-05-12 08:48:25 pramttl
Time limit is too strict. I submitted a O(n) solution in C++14 (memoized, recursive solution) still got TLE.
2015-05-12 05:19:56 Subhashis Bhowmik
My Ans is getting WA, Abeer's case worked, but @Riddhi, the output in your test case shud b 23 as my ans is saying. 6+9+8=23
EDIT: Sorry, didn't see consecutive, sorted the array first. My bad :p

Last edit: 2015-05-12 05:46:31
2014-12-07 22:45:55 Abeer Khan
Try this test case, Thanks to pero.
6 12
1 2 3 4 5 1
O/P
12
2014-09-23 10:37:56 Riddhi
Try this test case:
9 23
2 8 18 9 91 6 4 2 1

Output: 18
2012-09-01 17:37:04 AC Srinivas
similar problem ALIEN
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