GTW likes math

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 131072/131072 K (Java/Others)

Description

After attending the class given by Jin Longyu, who is a specially-graded teacher of Mathematics, GTW started to solve problems in a book titled “From Independent Recruitment to Olympiad”. Nevertheless, there are too many problems in the book yet GTW had a sheer number of things to do, such as dawdling away his time with his young girl. Thus, he asked you to solve these problems.

In each problem, you will be given a function whose form is like $f(x)=ax ^ 2 + bx + c$. Your assignment is to find the maximum value and the minimum value in the integer domain $[l, r]$.

Input

The first line of the input file is an integer $T$, indicating the number of test cases. ($T\leq 1000$)

In the following $T$ lines, each line indicates a test case, containing 5 integers, $a, b, c, l, r$. ($|a|, |b|, |c|\leq 100, |l|\leq |r|\leq 100$), whose meanings are given above.

Output

In each line of the output file, there should be exactly two integers, $max$ and $min$, indicating the maximum value and the minimum value of the given function in the integer domain $[l, r]$, respectively, of the test case respectively.

Sample Input

1 1 1 1 1 3

Sample Output

13 3
Hint
$f_1=3,f_2=7,f_3=13,max=13,min=3$

Hint

hujie

Source

BestCoder Round #66 (div.2)

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