All Tracks Math Number Theory Totient Function Problem

phi-phi-phi
Tag(s):

Easy, Math, Number Theory

Problem
Editorial
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Given n and k, calculate \(\varphi(\varphi(...\varphi(n)...))\), where \(\varphi\) applied exactly k times.

\(\varphi(n)\) is Euler's totient function. \(\varphi(1)=1\) by definition.

You can find the definition of Euler's totient function here.

Input format

The only line of input contains two integers n and k (\(1 \le n \le 10^{18}\), \(1 \le k \le 10^{18}\)).

Output format

Print one integer - answer to the problem.

Scoring

\(n \le 10^{3}\), \(k \le 10^{3}\) - 10 points

\(n \le 10^{6}\), \(k \le 10^{18}\) - 15 points

\(n \le 10^{12}\), \(k = 1\) - 10 points

\(n \le 10^{12}\), \(k \le 10^{18}\) - 10 points

\(n \le 10^{15}\), \(k = 1\) - 5 points

\(n \le 10^{15}\), \(k \le 10^{18}\) - 40 points

\(n \le 10^{18}\), \(k \le 10^{18}\) - 10 points

SAMPLE INPUT
12 2
SAMPLE OUTPUT
2
Explanation

\(\varphi(12) = 4\) and \(\varphi(4) = 2\)

So the answer is 2.

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: 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, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

October Clash '16

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