Queue Data Structure

Hotels Along the Croatian Coast

Time limit 1 second
Memory limit 128 MiB

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 data

In the first line there are integers n and m~(1 \le n \le 3 \cdot 10^5, 1 \le m < 2^{31}). In the next line there are n positive integers less than 10^6, representing the hotel values in the order they lie along the coast.

Output data

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


Input example #1
5 12
2 1 3 4 5
Output example #1