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 (1 ≤ n ≤ 300 000, 1 ≤ m < 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).