codeforces 404B Marathon（模拟）

Valera takes part in the Berland Marathon. The marathon race starts at the stadium that can be represented on the plane as a square whose lower left corner is located at point with coordinates (0, 0) and the length of the side
equals a meters. The sides of the square are parallel to coordinate axes.

As the length of the marathon race is very long, Valera needs to have extra drink during the race. The coach gives Valera a bottle of drink each d meters of the path. We know that Valera starts at the point with coordinates (0, 0) and
runs counter-clockwise. That is, when Valera covers a meters, he reaches the point with coordinates (a, 0). We also know that the length of the marathon race equals nd + 0.5meters.

Help Valera's coach determine where he should be located to help Valera. Specifically, determine the coordinates of Valera's positions when he covers d, 2·d, ..., n·d meters.

Input

The first line contains two space-separated real numbers a and d (1 ≤ a, d ≤ 105), given with precision
till 4 decimal digits after the decimal point. Number a denotes the length of the square's side that describes the stadium. Number d shows that after
each d meters Valera gets an extra drink.

The second line contains integer n (1 ≤ n ≤ 105) showing that Valera needs an extra drink n times.

Output

Print n lines, each line should contain two real numbers xi and yi,
separated by a space. Numbers xi and yi in the i-th line mean
that Valera is at point with coordinates (xi, <
4000
em>yi) after he covers i·d meters. Your
solution will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Note, that this problem have huge amount of output data. Please, do not use cout stream for output in this problem.

Example

Input

2 5
2

Output

1.0000000000 2.0000000000
2.0000000000 0.0000000000

Input

4.147 2.8819
6

Output

2.8819000000 0.0000000000
4.1470000000 1.6168000000
3.7953000000 4.1470000000
0.9134000000 4.1470000000
0.0000000000 2.1785000000
0.7034000000 0.0000000000

 【题解】

 大致题意：给定一个边长为a 的正方形，平行于x，y轴，左下角为（0,0）点，再给定一个长度d，现在规则是从正方形左下角出发，逆时针走，走到长度为d是输出其坐标位置，继续走，一共走n个d，输出每走d长度时所处的位置，保留十位小数。

 

 分析：

模拟起来也不是很难，一个for循环，i从1到n，表示走i个d长度，然后i*d的值mod周长，余数再除以边长，此时如果结果是0，则在x轴上，为1，则在x=a直线上，如果为2，就在y=a直线上，是3，就在y轴上，距离一算，就是结果，，这里用到了一个浮点数取模函数 double  m=fmod(a,b)，m是a mod b的余数。剩下的就很简单了，看代码。

【AC代码】

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<stack>
#include<math.h>
using namespace std;

double m,k;
int n;
double x,y;

int main()
{
while(~scanf("%lf%lf%d",&m,&k,&n))
{
double len=m*4;
for(int i=1;i<=n;++i)
{
double s=i*k;
s=fmod(s,len);
int p=1;
while(s-m>0)
{
s-=m;
p++;
}
if(p==1) x=s,y=0;
else if(p==2) x=m,y=s;
else if(p==3) x=m-s,y=m;
else if(p==4) x=0,y=m-s;

printf("%.10f %.10f\n",x,y);
}
}
return 0;
}