Alien Invader Yooni

Yooni, an alien, invades Ulsan, the central city of the world, to conquer the Earth. There are $N$ buildings in a row in Ulsan, and the height of the $i$-th building from the left is $h_i$.

Yooni has a plan to destroy Ulsan. Every day, Yooni rides a UFO over the city and fires a laser at the tallest building. A building hit by the laser becomes 1 shorter. If several buildings are tied for the tallest height that day, Yooni fires a laser at every one of them. If all buildings have already reached height $0$, Yooni stops firing lasers.

Yooni has followed the plan faithfully for $D$ days so far. Find the total number of lasers Yooni fired during those $D$ days.

The first line contains the number of buildings $N$ and the number of days $D$ that Yooni carried out the plan, separated by a space. ($1\le N\le 300\ 000$, $1\le D\le 300\ 000$)

The second line contains $N$ integers $h_i$, the heights of the buildings, separated by spaces. ($1\le h_i\le 300\ 000$)

Print the total number of lasers Yooni fired during the $D$ days. (Note that the answer may exceed the 32-bit integer range.)