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