Easy Sum Set Problem
Tag(s):

## Algorithms, Linear search, Searching algorithm, Very-Easy

Problem
Editorial
Analytics

In this problem, we define "set" is a collection of distinct numbers. For two sets $A$ and $B$, we define their sum set is a set $S(A, B) = \{a + b | a\in A, b \in B\}$. In other word,  set $S(A, B)$ contains all elements which can be represented as sum of an element in $A$ and an element in $B$. Given two sets $A, C$, your task is to find set $B$ of positive integers less than or equals $100$ with maximum size such that $S(A, B) = C$. It is guaranteed that there is unique such set.

Input Format

The first line contains $N$ denoting the number of elements in set $A$, the following line contains $N$ space-separated integers $a_i$ denoting the elements of set $A$.

The third line contains $M$ denoting the number of elements in set $C$, the following line contains $M$ space-separated integers $c_i$ denoting the elements of set $C$.

Output Format

Print all elements of $B$ in increasing order in a single line, separated by space.

Constraints

• $1 \le N, M \le 100$
• $1 \le a_i, c_i \le 100$

SAMPLE INPUT
2
1 2
3
3 4 5


SAMPLE OUTPUT
2 3

Explanation

If $e$ is an element of set $B$, then $e + 2$ is an element of set $C$, so we must have $e \le 3$. Clearly, $e$ cannot be $1$ because $1 + 1 = 2$ is not an element of set $C$. Therefore, $B = \{2, 3\}$.

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, TypeScript, Visual Basic

## CODE EDITOR

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## This Problem was Asked in Challenge Name

July Circuits '18

OTHER PROBLEMS OF THIS CHALLENGE
• Math > Basic Geometry
• Algorithms > Graphs
• Math > Number Theory
• Algorithms > Searching