CF1190A.Tokitsukaze and Discard Items

Recently, Tokitsukaze found an interesting game. Tokitsukaze had $n$ items at the beginning of this game. However, she thought there were too many items, so now she wants to discard $m$ ($1 \le m \le n$) special items of them.

These $n$ items are marked with indices from $1$ to $n$. In the beginning, the item with index $i$ is placed on the $i$-th position. Items are divided into several pages orderly, such that each page contains exactly $k$ positions and the last positions on the last page may be left empty.

Tokitsukaze would do the following operation: focus on the first special page that contains at least one special item, and at one time, Tokitsukaze would discard all special items on this page. After an item is discarded or moved, its old position would be empty, and then the item below it, if exists, would move up to this empty position. The movement may bring many items forward and even into previous pages, so Tokitsukaze would keep waiting until all the items stop moving, and then do the operation (i.e. check the special page and discard the special items) repeatedly until there is no item need to be discarded.

Consider the first example from the statement: $n=10$, $m=4$, $k=5$, $p=[3, 5, 7, 10]$. The are two pages. Initially, the first page is special (since it is the first page containing a special item). So Tokitsukaze discards the special items with indices $3$ and $5$. After, the first page remains to be special. It contains $[1, 2, 4, 6, 7]$, Tokitsukaze discards the special item with index $7$. After, the second page is special (since it is the first page containing a special item). It contains $[9, 10]$, Tokitsukaze discards the special item with index $10$.

Tokitsukaze wants to know the number of operations she would do in total.

最近，时雨发现了一个有趣的游戏。游戏开始时，时雨拥有 $n$ 个物品。但她觉得物品数量太多，因此现在她想要丢弃其中 $m$ 个（$1 \le m \le n$）特殊物品。

这 $n$ 个物品的编号为 $1$ 到 $n$。初始时，编号为 $i$ 的物品位于第 $i$ 个位置。物品按顺序被划分为若干页，每页恰好包含 $k$ 个位置，最后一页的末尾位置可能为空。

时雨将执行如下操作：首先定位第一个包含至少一个特殊物品的特殊页，然后一次性丢弃该页上的所有特殊物品。每当一个物品被丢弃或移动后，其原来的位置即变为空；若其下方存在物品，则该物品会向上移动至这个空位。这种移动可能导致大量物品前移，甚至跨页进入前面的页面。因此，时雨会持续等待，直至所有物品停止移动，再重复执行上述操作（即重新检查首个含特殊物品的页并丢弃该页所有特殊物品），直到没有物品需要被丢弃为止。

考虑题面中的第一个示例：$n=10$，$m=4$，$k=5$，$p=[3, 5, 7, 10]$。共分为两页。初始时，第一页是特殊页（因为它是首个包含特殊物品的页）。因此时雨丢弃编号为 $3$ 和 $5$ 的特殊物品。之后，第一页仍为特殊页，其上物品变为 $[1, 2, 4, 6, 7]$，时雨丢弃编号为 $7$ 的特殊物品。随后，第二页成为特殊页（因为此时它是首个包含特殊物品的页），其上物品为 $[9, 10]$，时雨丢弃编号为 $10$ 的特殊物品。

时雨想知道她总共需要执行多少次操作。

The first line contains three integers $n$, $m$ and $k$ ($1 \le n \le 10^{18}$, $1 \le m \le 10^5$, $1 \le m, k \le n$) — the number of items, the number of special items to be discarded and the number of positions in each page.

The second line contains $m$ distinct integers $p_1, p_2, \ldots, p_m$ ($1 \le p_1 \lt p_2 \lt \ldots \lt p_m \le n$) — the indices of special items which should be discarded.

第一行包含三个整数 $n$、$m$ 和 $k$（$1 \le n \le 10^{18}$，$1 \le m \le 10^5$，$1 \le m, k \le n$）—— 分别表示物品总数、需丢弃的特殊物品数量以及每页的位置数。

第二行包含 $m$ 个互不相同的整数 $p_1, p_2, \ldots, p_m$（$1 \le p_1 \lt p_2 \lt \ldots \lt p_m \le n$）—— 表示需丢弃的特殊物品的索引。

Print a single integer — the number of operations that Tokitsukaze would do in total.

输出一个整数——Tokitsukaze 总共执行的操作次数。

For the first example:

• In the first operation, Tokitsukaze would focus on the first page $[1, 2, 3, 4, 5]$ and discard items with indices $3$ and $5$;
• In the second operation, Tokitsukaze would focus on the first page $[1, 2, 4, 6, 7]$ and discard item with index $7$;
• In the third operation, Tokitsukaze would focus on the second page $[9, 10]$ and discard item with index $10$.

For the second example, Tokitsukaze would focus on the second page $[6, 7, 8, 9, 10]$ and discard all special items at once.

对于第一个例子：

• 在第一次操作中，Tokitsukaze 将聚焦于第一页 $[1, 2, 3, 4, 5]$，并丢弃索引为 $3$ 和 $5$ 的物品；
• 在第二次操作中，Tokitsukaze 将聚焦于第一页 $[1, 2, 4, 6, 7]$，并丢弃索引为 $7$ 的物品；
• 在第三次操作中，Tokitsukaze 将聚焦于第二页 $[9, 10]$，并丢弃索引为 $10$ 的物品。

对于第二个例子，Tokitsukaze 将聚焦于第二页 $[6, 7, 8, 9, 10]$，并一次性丢弃所有特殊物品。