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ZOJ Problem Set - 1912

Time Limit: 2 Seconds      Memory Limit: 65536 KB

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.

Sample Input

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

Sample Output


don't know
don't know

don't know
don't know


don't know


don't know
don't know

Source: University of Waterloo Local Contest 2002.09.28
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