It's another Startcup, 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. In the first example, we can buy 100 of each size.