A11231 | Ordering T-Shirts

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 will begin with two integers $N$ and $C$ ( $1<=N<=2·10^{5}$ , $1<=C$ ), the number of T-shirt sizes and number of T-shirts to be awarded, respectively.

Following this is a line with $2·N-1$ integers, $s_{1}$ through $s_{2·N-1}$ $(0<=s_{i}<=10^{8})$ . For odd $i$ , $s_{i}$ indicates the number of contestants desiring T-shirt size $((i+1)/2)$ . For even $i$ , $s_{i}$ 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.

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