Xeroxinator

Doctor Heinz Fufelschmertz was tired of standing in lines, so he built a xeroxinator, a device that makes clones of people. He now sends his clones to stand in lines in his place. Unfortunately, the device malfunctioned. Now too many clones of Heinz are being made, and all of them go to the post office.

Today the post office is open for $n$ minutes, numbered from 1 to $n$. At the start of minute $i$, $a_i$ clones of Fufelschmertz enter the post office and join the end of the queue. In one minute, the post office serves at most $b$ clones. If the queue has at least $b$ clones, the first $b$ of them are served. Otherwise, everyone in the queue is served. All clones served in minute $i$ leave at the end of minute $i$. The post office closes at the end of minute $n$. Clones who were not served wait for one more minute, complain, and then leave. Help Heinz compute the total time all clones spend in the post office.

Note that a clone who enters at the start of minute $i$ and leaves at the end of minute $i$ spent one minute in the post office.

The first line contains two integers $n$ and $b$, the number of minutes the post office is open and the maximum number of clones served per minute ($1 \le n \le 100000$, $1 \le b \le 10^8$).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$, where $a_i$ is the number of clones arriving at the start of minute $i$ ($0 \le a_i \le 10^8$).

Print one integer: the total time all clones spend in the post office.