简单模拟 CodeForces - 404B Marathon

B. Marathon

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 + 0.5 meters.

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 x_i and y_i, separated by a space. Numbers x_i and y_i in the i-th line mean that Valera is at point with coordinates (x_i, y_i) 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.

Examples

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

题目大意：围着矩形跑马拉松，每隔距离d需要喝一次水，确定n次喝水中每次的位置。

其实这是道水题，直接模拟一下就行了，但是要格外注意到精度问题，遇上精度误差有时会调试很久白白浪费时间。

同时像这种矩形边跑的模拟我也不是很熟悉，需要多加练习，没事拿出来看看。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>

using namespace std;

int main()
{
    double k, a, d;
    long long int c, n, i;
    scanf("%lf%lf", &a, &d);
    scanf("%I64d", &n);
    for(i = 1;i <= n; i++) {
        k = i*d;
        c = k/a;
        k = k - c*a;
//        printf("k = %f\n", k);
//        printf("c = %d\n", c);
//        printf("a = %f\n", a);
        if(c % 4 == 0)
            printf("%f 0.0000\n", k);
        if(c % 4 == 1)
            printf("%f %f\n", a, k);
         if(c % 4 == 2)
            printf("%f %f\n", (a-k), a);
         if(c % 4 == 3)
            printf("0.0000 %f\n", (a-k));
    }
    return 0;
}