Codeforces 518C Anya and Smartphone【思维+模拟】

C. Anya and Smartphone time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output

Anya has bought a new smartphone that uses Berdroid operating system. The smartphone menu has exactly n applications, each application has its own icon. The icons are located on different screens, one screen contains k icons. The icons from the first to the k-th one are located on the first screen, from the (k + 1)-th to the 2k-th ones are on the second screen and so on (the last screen may be partially empty).

Initially the smartphone menu is showing the screen number 1. To launch the application with the icon located on the screen t, Anya needs to make the following gestures: first she scrolls to the required screen number t, by making t - 1 gestures (if the icon is on the screen t), and then make another gesture — press the icon of the required application exactly once to launch it.

After the application is launched, the menu returns to the first screen. That is, to launch the next application you need to scroll through the menu again starting from the screen number 1.

All applications are numbered from 1 to n. We know a certain order in which the icons of the applications are located in the menu at the beginning, but it changes as long as you use the operating system. Berdroid is intelligent system, so it changes the order of the icons by moving the more frequently used icons to the beginning of the list. Formally, right after an application is launched, Berdroid swaps the application icon and the icon of a preceding application (that is, the icon of an application on the position that is smaller by one in the order of menu). The preceding icon may possibly be located on the adjacent screen. The only exception is when the icon of the launched application already occupies the first place, in this case the icon arrangement doesn't change.

Anya has planned the order in which she will launch applications. How many gestures should Anya make to launch the applications in the planned order?

Note that one application may be launched multiple times.

Input

The first line of the input contains three numbers n, m, k (1 ≤ n, m, k ≤ 10⁵) — the number of applications that Anya has on her smartphone, the number of applications that will be launched and the number of icons that are located on the same screen.

The next line contains n integers, permutation a₁, a₂, ..., a_n — the initial order of icons from left to right in the menu (from the first to the last one), a_i —  is the id of the application, whose icon goes i-th in the menu. Each integer from 1 to n occurs exactly once among a_i.

The third line contains m integers b₁, b₂, ..., b_m(1 ≤ b_i ≤ n) — the ids of the launched applications in the planned order. One application may be launched multiple times.

Output

Print a single number — the number of gestures that Anya needs to make to launch all the applications in the desired order.

Examples Input 8 3 3 1 2 3 4 5 6 7 8 7 8 1 Output 7 Input 5 4 2 3 1 5 2 4 4 4 4 4 Output 8 Note

In the first test the initial configuration looks like (123)(456)(78), that is, the first screen contains icons of applications 1, 2, 3, the second screen contains icons 4, 5, 6, the third screen contains icons 7, 8.

After application 7 is launched, we get the new arrangement of the icons — (123)(457)(68). To launch it Anya makes 3 gestures.

After application 8 is launched, we get configuration (123)(457)(86). To launch it Anya makes 3 gestures.

After application 1 is launched, the arrangement of icons in the menu doesn't change. To launch it Anya makes 1 gesture.

In total, Anya makes 7 gestures.

题目大意：

给你N个数，其中有M个按照顺序打开的程序。

每页有K个程序。

最后一页程序不必要排满。

每次打开程序的时候，要滑动屏幕，然后点击程序。每一次滑动屏幕花费1时间，点击程序花费1时间。

打开一个程序之后，这个程序会和前边编号的程序进行交换位子（如果是第一个程序就不必要了）。

问将这M个程序都打开一共需要多少时间。

思路：

模拟即可，维护两个数组，pos【i】，表示值为i的程序在的位子编号。

以及contz【i】，表示位子i需要进行的操作次数。

那么过程维护模拟即可。

Ac代码：

#include<stdio.h> #include<string.h> #include<algorithm> using namespace std; int id[100050]; int contz[100050]; int pos[100050]; int main() { int n,m,k; while(~scanf("%d%d%d",&n,&m,&k)) { for(int i=1;i<=n;i++)scanf("%d",&id[i]),pos[id[i]]=i; int bb=1; int cnt=0; for(int i=1;i<=n;i++) { if(cnt<k) { contz[i]=bb; cnt++; } else { bb++; contz[i]=bb; cnt=1; } } __int64 output=0; while(m--) { int x; scanf("%d",&x); output+=contz[pos[x]]; int pre=pos[x]-1; int idpre=id[pos[x]-1]; if(pos[x]!=1) { swap(id[pos[x]],id[pos[x]-1]); swap(pos[idpre],pos[x]); } } printf("%I64d\n",output); } }