TLE '17 Contest 7 P3 - Countless Calculator Computations

Points: 7 (partial)

Time limit: 1.0s

Java 2.0s

Python 3.0s

Memory limit: 256M

Author:

leonchen0613

Problem type

Leon is using a very powerful calculator.

Leon likes to play with calculators whenever he gets bored in class. Such fascinating devices! One day, an intriguing problem occurred to him:

If the equation $X^{X^{X^\cdots}}=Z$ ~X^{X^{X^\cdots}}=Z~ contains $Y$ ~Y~ number of $X$ ~X~'s, then given the values of $Y$ ~Y~ and $Z$ ~Z~, what is the approximate value of $X$ ~X~?

Leon is tasked with $Q$ ~Q~ queries regarding this problem. Apparently, he didn't perform these countless calculator computations well enough.

Can you help him?

Input Specification

The first line contains integer $Q$ ~Q~ $(1 \le Q \le 20\,000)$ ~(1 \le Q \le 20\,000)~, the number of queries.

The following $Q$ ~Q~ lines each contain two space-separated integers $Y_i$ ~Y_i~ $(2 \le Y_i \le 100)$ ~(2 \le Y_i \le 100)~ and $Z_i$ ~Z_i~ $(1 \le Z_i \le 2^{31}-1)$ ~(1 \le Z_i \le 2^{31}-1)~.

Output Specification

For each query, output the approximate value of $X_i$ ~X_i~ on its own line, accurate within an absolute error of $10^{-5}$ ~10^{-5}~.

For $50\%$ ~50\%~ of the points, $X_i$ ~X_i~ may be accurate within an absolute error of $10^{-1}$ ~10^{-1}~.

Sample Input

Sample Output

1.414213562
1.4484039
1.99999

Comments

0

tmago3 commented on Jan. 18, 2024, 6:51 a.m.

how do we get the first answer