{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"In a billiard table with horizontal side a inches and vertical side b inches, a ball is launched from the middle of the table. After s \u0026gt; 0 seconds the ball returns to the point from which it was launched, after having made m bounces off the vertical sides and n bounces off the horizontal sides of the table. Find the launching angle A (measured from the horizontal), which will be between 0 and 90 degrees inclusive, and the initial velocity of the ball. \r\u003cbr\u003eAssume 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. \r\u003cbr\u003e"}},{"title":"Input","value":{"format":"HTML","content":"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. \r\u003cbr\u003eInput is terminated by a line containing five zeroes. \r\u003cbr\u003e"}},{"title":"Output","value":{"format":"HTML","content":"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. "}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e100 100 1 1 1\r\n200 100 5 3 4\r\n201 132 48 1900 156\r\n0 0 0 0 0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e45.00 141.42\r\n33.69 144.22\r\n3.09 7967.81\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}