UVA10387 Billiard

Description

In a billiard table with horizontal side a inches and vertical sideb inches, a ball is launched from the middle of the table. Afters > 0 seconds the ball returns to the point from which it was launched, after having madem bounces off the vertical sides and n bounces off the horizontal sides of the table. Find the launching angleA (measured from the horizontal), which will be between 0 and 90 degrees inclusive, and the initial velocity of the ball.

Assume that the collisions with a side are elastic (no energy loss), and thus the velocity component of the ball parallel to each side remains unchanged. Also, assume the ball has a radius of zero. Remember that, unlike pool tables, billiard tables have no pockets.

Input

Input consists of a sequence of lines, each containing five nonnegative integers separated by whitespace. The five numbers are: a, b, s, m, and n, respectively. All numbers are positive integers not greater than 10000.

Input is terminated by a line containing five zeroes.

Output

For each input line except the last, output a line containing two real numbers (accurate to two decimal places) separated by a single space. The first number is the measure of the angle A in degrees and the second is the velocity of the ball measured in inches per second, according to the description above.

Sample Input

100 100 1 1 1200 100 5 3 4201 132 48 1900 1560 0 0 0 0

Sample Output

45.00 141.4233.69 144.223.09 7967.81题目的意思就是在一张长ａ宽ｂ的桌子正中心有一个球，和水平方向以某个夹角，某个速度打出，在ｓ秒后回到原来位置并且　和水平方向撞了ｍ次，垂直方向撞了ｎ次，，给出桌子长宽，时间，水平碰的次数，垂直碰的次数。。。求夹角和速度。。。就是根据长宽，时间和碰的次数，算出水平运动了多远，垂直运动了多久，再用三角函数求角度和速度。。ＡＣ代码：
#include<stdio.h>#include<cmath>int main () {double a,b,s,m,n;double cd,rd,d,de;double crate,rrate,rate;while (scanf("%lf%lf%lf%lf%lf",&a,&b,&s,&m,&n)) {if(a == 0 && b == 0 && s == 0 && m == 0 && n == 0)break;cd = m * a;rd = n * b;d = sqrt(cd * cd + rd *rd);rate = d /s;de = atan(rd/cd);de = de * 180 / acos(-1);printf("%.2lf %.2lf\n",de,rate);}}