All Tracks Algorithms Searching Binary Search Problem

Picu Bank
Tag(s):

Algorithms, Binary search algorithm, Easy, Mathematics, Searching algorithm

Problem
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You have $$D$$ dollars with you. You want to put it into a Bank, namely Picu Bank. This bank has a peculiar behavior for interest. Regardless of the Bank deposit amount, every month it adds $$A$$ dollars to your bank account and this continues till $$M$$ months. Exaxtly on $$ M+1 $$ months, it adds $$B$$ dollars $$ (B < A) $$ to your bank account. This scanario repeats again in same manner.( i.e on the $$ (M+2)^{th}$$ month $$A$$ dollars are added, and so on.. ). Your task is to find out how many months does it take for the dollar amount to reach at least $$X$$, in the bank account .    

Input:

Input starts with an integer $$ T (1 \le T \le 100000) $$, denoting the number of test cases.  Each case starts with 5 integers $$D, A, M, B$$ , and $$ X $$ as described in problem statement.

 

Constraints:

  • $$ 1 \le D,M,X \le 10^9 $$
  • $$ 1 \le B < A \le 10^9 $$ 

Output:

For each case of input minimum number of months needed to reach dollar value of at least X in a single line.

Note that the Expected Output feature of Custom Invocation is not supported for this contest. 

SAMPLE INPUT
2
2 5 4 3 51
2 5 4 3 46
SAMPLE OUTPUT
11
10
Explanation

 

Time Limit: 1.0 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

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This Problem was Asked in

HackerEarth

Challenge Name

August Circuits '18

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