codeforces404 B. Marathon【简单几何】

B. Marathon

time limit per test1 second
memory limit per test256 megabytes

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 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, 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.

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
题意: 已知一人再跑马拉松,起点为(0,0),围绕这一个正方形的赛道逆时针跑,每隔d单位的距离,就要送一次水,一共n次,问你每次送水的坐标

分析: 因为起点固定,我们每次求出送第i次水的需要的距离然后看在哪就行,如果大于4*a,就减去,因为跑一圈还在原点,然后O(1),的判断在哪条边即可

参考代码

#include

using namespace std;

int main(){
    double a,d;cin>>a>>d;
    int n;cin>>n;
    double x = 0,y = 0;
    double quan = a*4;
    double ling = 0;
    for (int i = 1;i <= n;i++) {
        double to = d*i;
        to -= ((long long ) (to/quan)) * quan;
        if(to > 3*a) {
            printf("%.10f %.10f\n",ling,4*a - to);
        } else if (to > 2*a) {
            printf("%.10f %.10f\n",3*a - to,a);
        } else if (to > a) {
            printf("%.10f %.10f\n",a,to - a);
        } else {
            printf("%.10f %.10f\n",to,ling);
        }
    }
    return 0;
}
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