F. Ordering T-Shirts
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

It's another Start[c]up, and that means there are T-shirts to order. In order to make sure T-shirts are shipped as soon as possible, we've decided that this year we're going to order all of the necessary T-shirts before the actual competition. The top C contestants are going to be awarded T-shirts, but we obviously don't know which contestants that will be. The plan is to get the T-Shirt sizes of all contestants before the actual competition, and then order enough T-shirts so that no matter who is in the top C we'll have T-shirts available in order to award them.

In order to get the T-shirt sizes of the contestants, we will send out a survey. The survey will allow contestants to either specify a single desired T-shirt size, or two adjacent T-shirt sizes. If a contestant specifies two sizes, it means that they can be awarded either size.

As you can probably tell, this plan could require ordering a lot of unnecessary T-shirts. We'd like your help to determine the minimum number of T-shirts we'll need to order to ensure that we'll be able to award T-shirts no matter the outcome of the competition.

Input

Input will begin with two integers N and C (1 ≤ N ≤ 2·105, 1 ≤ C), the number of T-shirt sizes and number of T-shirts to be awarded, respectively.

Following this is a line with N - 1 integers, s1 through sN - 1 (0 ≤ si ≤ 108). For odd i, si indicates the number of contestants desiring T-shirt size ((i + 1) / 2). For even i, si indicates the number of contestants okay receiving either of T-shirt sizes (i / 2) and (i / 2 + 1). C will not exceed the total number of contestants.

Output

Print the minimum number of T-shirts we need to buy.

Examples
Input
2 200100 250 100
Output
200
Input
4 16088 69 62 29 58 52 44
Output
314
Note

In the first example, we can buy 100 of each size.