Equations

Tags:
Time Limit:  1 s      Memory Limit:   128 MB
Submission：0     AC：0     Score：100.00

Description

Given 2 equations on the variables

x

and

y

, solve for

x

and

y

.

The first line of input contains N, the number of test cases. Each test case consists of two equations, each on a separate line. An empty line separates cases. An equation consists of two or more terms separated by addition, subtraction, or equality operators. A term is an integer, or a variable name (x or y) optionally preceded by a minus sign or an integer coefficient. There is exactly one equality operator. All operators are surrounded by spaces, and there are no spaces within terms. For each case, print two lines, giving the values of x and y as rationals in simplest terms. If x or y has no unique rational value such that both equations hold, print "don't know" for its value. Print an empty line between cases.

Samples

input
7 2x + 3y = x 5 = x + y + 3 2x + 3y = 0 10x = -15y 2x + 3y = 0 10x = -15y + 1 x = 1 3x = 6y 2x = 3x + -x + y x + y = x + y 2x = -3 -2y = 3 1 = 2 x = 3
output
3 -1 don't know don't know don't know don't know 1 1/2 don't know 0 -3/2 -3/2 don't know don't know