Hotels Along the Croatian Coast#10682

Hotels Along the Croatian Coast

1 second
128 megabytes
Very easy

Along the beautiful Adriatic coast, there are hotels. Each hotel has its cost in euros.

Petr won euros in the lottery. Now he wants to buy a sequence of consecutive hotels one after another so that the sum of the costs of these consecutive hotels is as large as possible, but does not exceed .

You need to calculate this maximum possible total cost.

Input

The first line contains two integers and m~(1 \le n \le 3 \cdot 10^5, 1 \le m < 2^{31}). The next line contains positive integers less than 10^6, representing the costs of the hotels in the order they are located along the coast.

Output

Print the desired maximum cost (it will be greater than in all tests).

Examples

Example 1

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