Problem K
Scientific Grading
You recently started working as a TA (teaching assistant) for your university’s Scientific Computing class. Today, Professor introduced the scientific notation, where numbers are written in the form $m \times 10^ n$ with a real number $m$ (the significand) and an integer $n$ (the exponent). At the end of class, she gave students the following assignment.
Given two numbers $x$, $y$ in scientific notation, perform the following four arithmetic operations:

$x + y$

$x  y$

$x \times y$

$x / y$
As a strict grader, you decided to write a program to grade students’ answers. You mark a solution correct if and only if both relative and absolute errors are less than $10^{9}$ (not including $10^{9}$). If the correct answer is $0$, then $0$ is the only acceptable answer. Otherwise, a student’s answer $z$ will be compared to the correct answer $\tilde{z}$, and the relative and absolute errors are computed as $\frac{z  \tilde{z}}{\tilde{z}}$ and $z  \tilde{z}$, respectively.
Input
The first line of input contains the value of $x$, and the second line contains the value of $y$. The next four lines contain a student’s answer to $x+y$, $xy$, $x \times y$, and $x/y$. All numbers are in the form of <SIGNIFICAND>e<EXPONENT>. The significand $m$ starts with a sign (+ or ), followed by one digit, a period (.), and exactly nine digits. The exponent $n$ also starts with a sign (+ or ) and is followed by an integer between $0$ and $10^9$, inclusively. The value is computed by $m \times 10^ n$. The value $0$ is always represented as +0.000000000e+0, and for any nonzero values the first digit of their significand is not $0$. It is guaranteed that $x$ and $y$ are both nonzero.
Output
For each student solution, output Correct if it is considered correct and Incorrect otherwise. The first line of output indicates if the student’s solution to $x+y$ is correct, the second line indicates if their solution to $xy$ is correct, the third line indicates if their solution to $x \times y$ is correct, and the fourth line indicates if their solution to $x/y$ is correct.
Sample Input 1  Sample Output 1 

+2.000000000e+1 +3.000000000e+2 +3.200000000e+2 2.800000000e+2 +6.000000000e+3 +6.666666667e2 
Correct Correct Correct Correct 
Sample Input 2  Sample Output 2 

+1.000000000e1 +1.000000000e1 +2.000000003e1 +1.000000000e18 +1.000000002e2 +1.000000001e+0 
Incorrect Incorrect Incorrect Incorrect 