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July 9 - ADA Training

Hotels Along the Croatian Coast

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

Peter 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 there are integers n and m (1n300 000, 1m < 231). In the next line there are n positive integers 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).

Time limit 1 second
Memory limit 128 MiB
Input example #1
5 12
2 1 3 4 5
Output example #1
12