Tokitsukaze and Discard Items

题意翻译

题意：最近，T发现了一个有趣的游戏。在游戏开始，T有n个数（1~n）。这n个数每k个被分为一组（最后一组可能不到k个）。现在她想拿出m个数 p1, p2,..., pm（输入保证该序列为升序）。她会从1到n逐个看，如果发现了她想要的数，那么她会将这组数中所有她想要的都取走，算作一次操作。（如图） 一次操作结束后，数列中的数会自动左移补上被拿出的数的位置，但数值不变。问：经过多少次操作后，T能取到所有她想要的数？ ------------ 输入：第一行：n（1≤n≤10^18), m(1≤m≤10^5), k(1≤m,k≤n) ------------ 第二行：m个数p1, p2, ... , pm(1≤p1<p2<...<pm≤n) 输出：T将进行的操作数

题目描述

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.

输入输出格式

输入格式

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 < p_2 < \ldots < p_m \le n $ ) — the indices of special items which should be discarded.

输出格式

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

输入输出样例

输入样例 #1

10 4 5
3 5 7 10

输出样例 #1

3

输入样例 #2

13 4 5
7 8 9 10

输出样例 #2

1

说明

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.