151. Construct a triangle

time limit per test: 0.25 sec.
memory limit per test: 4096 KB
input: standard input
output: standard output

Find coordinates of any triangle ABC if it is know that |AB|=c, |AC|=b, |AM|=m, AM is a median of triangle.

There are three real numbers in input: c, b, m (0<c,b,m<=10^3) separated by a space. Length of the fractional part of each number is not greater than 2 digits.

If solution exists, write three lines. Write coordinates of point A to first line, coordinates of B to second line and coordinates of C to third line. Separate numbers by a space; absolute value of each coordinate must not exceed 10^4. Write numbers with 5 digits after decimal point. If there is no solution, write "Mission impossible"

Sample test(s)

5 5 3

0.00000 3.00000
-4.00000 0.00000
4.00000 0.00000

Author:Michael R. Mirzayanov
Resource:Saratov Subregional School Team Contest, 2002
Date:Spring, 2002