CF859F.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.

又到了 Start[c]up 比赛的时间，这意味着需要订购 T 恤。为了尽快发货，我们决定今年在正式比赛开始前就提前订购所有必需的 T 恤。排名前 C 名的参赛者将获得 T 恤，但我们显然还不知道最终哪些参赛者会进入前 C 名。我们的计划是：在正式比赛前先收集所有参赛者的 T 恤尺码信息，然后订购足够数量的 T 恤，以确保无论最终哪 C 名参赛者获奖，我们都拥有对应尺码的 T 恤可供发放。

为收集参赛者的 T 恤尺码，我们将发送一份问卷调查。该问卷允许每位参赛者指定一个期望的 T 恤尺码，或指定两个相邻的 T 恤尺码。若某位参赛者指定了两个尺码，则表示他/她可接受其中任意一个尺码。

你可能已经意识到，这一方案可能导致订购大量不必要的 T 恤。我们希望你能帮助我们确定：为确保无论比赛结果如何都能成功发放 T 恤，所需订购的 T 恤的最少数量是多少？

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 2·N - 1 integers, _s_1 through _s_2·N - 1 (0 ≤ s__i ≤ 108). 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.

输入的第一行包含两个整数 $N$ 和 $C$（$1 \leq N \leq 2\cdot10^5$，$1 \leq C$），分别表示 T 恤尺码的种类数和待发放的 T 恤件数。

接下来的一行包含 $2\cdot N - 1$ 个整数 $s_1$ 到 $s_{2\cdot N - 1}$（$0 \leq s_i \leq 10^8$）。

• 当 $i$ 为奇数时，$s_i$ 表示希望获得第 $\frac{i+1}{2}$ 号尺码 T 恤的参赛者人数；
• 当 $i$ 为偶数时，$s_i$ 表示可接受第 $\frac{i}{2}$ 号或第 $\frac{i}{2} + 1$ 号尺码 T 恤的参赛者人数。
  保证 $C$ 不超过参赛者总人数。

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

输出我们需要购买的 T 恤的最少数量。

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

在第一个示例中，我们可以每种尺寸各购买 100 个。