CF1765D.Watch the Videos

Monocarp wants to watch $n$ videos. Each video is only one minute long, but its size may be arbitrary. The $i$-th video has the size $a_i$ megabytes. All videos are published on the Internet. A video should be downloaded before it can be watched. Monocarp has poor Internet connection — it takes exactly $1$ minute to download $1$ megabyte of data, so it will require $a_i$ minutes to download the $i$-th video.

Monocarp's computer has a hard disk of $m$ megabytes. The disk is used to store the downloaded videos. Once Monocarp starts the download of a video of size $s$, the $s$ megabytes are immediately reserved on a hard disk. If there are less than $s$ megabytes left, the download cannot be started until the required space is freed. Each single video can be stored on the hard disk, since $a_i \le m$ for all $i$. Once the download is started, it cannot be interrupted. It is not allowed to run two or more downloads in parallel.

Once a video is fully downloaded to the hard disk, Monocarp can watch it. Watching each video takes exactly $1$ minute and does not occupy the Internet connection, so Monocarp can start downloading another video while watching the current one.

When Monocarp finishes watching a video, he doesn't need it on the hard disk anymore, so he can delete the video, instantly freeing the space it occupied on a hard disk. Deleting a video takes negligible time.

Monocarp wants to watch all $n$ videos as quickly as possible. The order of watching does not matter, since Monocarp needs to watch all of them anyway. Please calculate the minimum possible time required for that.

Monocarp 想要观看 $n$ 个视频。每个视频时长恰好为 1 分钟，但其大小可以是任意的。第 $i$ 个视频的大小为 $a_i$ 兆字节（MB）。所有视频均发布在互联网上，而一个视频必须先被下载，才能被观看。Monocarp 的网络连接较差——下载数据的速度恰好为每分钟 1 兆字节，因此下载第 $i$ 个视频需要 $a_i$ 分钟。

Monocarp 的电脑硬盘容量为 $m$ 兆字节，用于存储已下载的视频。一旦 Monocarp 开始下载一个大小为 $s$ 的视频，硬盘上会立即预留出 $s$ 兆字节的空间。若剩余空间不足 $s$ 兆字节，则无法启动该下载，直至释放出所需空间为止。由于对所有 $i$ 均有 $a_i \le m$，因此每个视频均可单独存入硬盘。一旦下载开始，便不可中断。同时，不允许并行运行两个或更多下载任务。

当一个视频被完整下载至硬盘后，Monocarp 即可开始观看它。观看每个视频恰好耗时 1 分钟，且不占用网络连接，因此 Monocarp 可以在观看当前视频的同时，开始下载另一个视频。

当 Monocarp 观看完一个视频后，便不再需要该视频保存在硬盘上，因此他可以立即将其删除，从而瞬时释放其所占的硬盘空间。删除视频所耗时间可忽略不计。

Monocarp 希望以尽可能短的时间观看全部 $n$ 个视频。观看顺序无关紧要，因为 Monocarp 最终必须观看所有视频。请计算完成这一目标所需的最短可能时间。

The first line contains two integers $n$ and $m$ ($1 \le n \le 2 \cdot 10^5$; $1 \le m \le 10^9$) — the number of videos Monocarp wants to watch and the size of the hard disk, respectively.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le m$) — the sizes of the videos.

第一行包含两个整数 $n$ 和 $m$（$1 \le n \le 2 \cdot 10^5$；$1 \le m \le 10^9$）—— 分别表示 Monocarp 想观看的视频数量以及硬盘容量。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1 \le a_i \le m$）—— 表示各视频的大小。

Print one integer — the minimum time required to watch all $n$ videos.

输出一个整数——观看全部 $n$ 个视频所需的最短时间。