CF1675G.Sorting Pancakes

Nastya baked $m$ pancakes and spread them on $n$ dishes. The dishes are in a row and numbered from left to right. She put $a_i$ pancakes on the dish with the index $i$.

Seeing the dishes, Vlad decided to bring order to the stacks and move some pancakes. In one move, he can shift one pancake from any dish to the closest one, that is, select the dish $i$ ($a_i \gt 0$) and do one of the following:

• if $i \gt 1$, put the pancake on a dish with the previous index, after this move $a_i = a_i - 1$ and $a_{i - 1} = a_{i - 1} + 1$;
• if $i \lt n$, put the pancake on a dish with the following index, after this move $a_i = a_i - 1$ and $a_{i + 1} = a_{i + 1} + 1$.

Vlad wants to make the array $a$non-increasing, after moving as few pancakes as possible. Help him find the minimum number of moves needed for this.

The array $a=[a_1, a_2,\dots,a_n]$ is called non-increasing if $a_i \ge a_{i+1}$ for all $i$ from $1$ to $n-1$.

娜斯佳烤了 $m$ 个煎饼，并将它们分放在 $n$ 个盘子上。这些盘子排成一行，从左到右依次编号。她在编号为 $i$ 的盘子上放了 $a_i$ 个煎饼。

弗拉德看到这些盘子后，决定对煎饼堆进行整理，移动其中一些煎饼。在一次操作中，他可以将一个煎饼从任意一个盘子移动到与其相邻的盘子上，即：选择一个满足 $a_i > 0$ 的盘子 $i$，并执行以下两种操作之一：

• 若 $i > 1$，则将该煎饼移到前一个编号的盘子上；操作后有 $a_i = a_i - 1$ 且 $a_{i - 1} = a_{i - 1} + 1$；
• 若 $i < n$，则将该煎饼移到后一个编号的盘子上；操作后有 $a_i = a_i - 1$ 且 $a_{i + 1} = a_{i + 1} + 1$。

弗拉德希望经过尽可能少的操作次数，使得数组 $a$ 变为非递增序列。请你帮他求出达成这一目标所需的最少操作次数。

数组 $a=[a_1, a_2,\dots,a_n]$ 称为非递增的，当且仅当对所有 $i = 1, 2, \dots, n-1$，均满足 $a_i \ge a_{i+1}$。

The first line of the input contains two numbers $n$ and $m$ ($1 \le n, m \le 250$) — the number of dishes and the number of pancakes, respectively.

The second line contains $n$ numbers $a_i$ ($0 \le a_i \le m$), the sum of all $a_i$ is equal to $m$.

输入的第一行包含两个数字 $n$ 和 $m$（$1 \le n, m \le 250$）——分别表示菜肴的数量和煎饼的总数。

第二行包含 $n$ 个数字 $a_i$（$0 \le a_i \le m$），所有 $a_i$ 的总和等于 $m$。

Print a single number: the minimum number of moves required to make the array $a$ non-increasing.

输出一个整数：使数组 $a$ 变为非递增序列所需的最少操作次数。

In the first example, you first need to move the pancake from the dish $1$, after which $a = [4, 4, 2, 3, 3, 3]$. After that, you need to move the pancake from the dish $2$ to the dish $3$ and the array will become non-growing $a = [4, 3, 3, 3, 3, 3]$.

在第一个例子中，你需要先将盘子 $1$ 上的煎饼移走，之后数组变为 $a = [4, 4, 2, 3, 3, 3]$。接着，你需要将盘子 $2$ 上的煎饼移到盘子 $3$ 上，此时数组将变为非递增序列 $a = [4, 3, 3, 3, 3, 3]$。