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.