## DMOPC '18 Contest 5 P0 - A Digital Art Problem

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Points: 3
Time limit: 2.0s
Memory limit: 64M

Author:
Problem type
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

The Multiply, Screen, and Overlay blend modes in image manipulation programs such as Photoshop are very useful when making digital art. If you apply one of these modes to a base colour and a top colour, a resulting colour is produced. Colours have three components: , , and , which can have any real value from to (completely dark to completely light) inclusive, and modes operate on each component separately. Let's call a component of the base colour and the same component of the top colour .

If you apply the Multiply mode, the resulting component will be . As this produces a darker colour, it is good for drawing shadows.

If you apply the Screen mode, the resulting component will be . As this produces a lighter colour, it is good for drawing highlights.

The Overlay mode produces different results depending on the base component. If this component is less than , the resulting value is . Otherwise, the resulting value is . As this makes dark colours darker and light colours lighter, it is good for adding contrast.

Given a blend mode and each component of the base and top colours, please find the resulting colour.

#### Input Specification

The first line will contain one of the following strings: Multiply, Screen, or Overlay, the blend mode.
The second line will contain 3 space-separated real numbers: , , and representing each component of the base colour.
The third and final line will contain 3 space-separated real numbers: , , and representing each component of the top colour.

#### Output Specification

Output 3 space-separated real numbers on one line: the , , and of the resulting colour.
Your answer will be judged correct if it has an absolute or relative error less than or equal to .

#### Sample Input

Multiply
0.30 0.22 0.90
0.52 0.12 0.03

#### Sample Output

0.156000 0.026400 0.027000