TLE '17 Contest 7 P3 - Countless Calculator Computations - Olympiads Online Judge

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 $X^{X^{X^\cdots}}=Z$ $X^{X^{X^{\dots}}} = Z$ 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 $Q$ $Q$ $(1 \le Q \le 20\,000)$ $(1 \leq Q \leq 20 000)$ , the number of queries.

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

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

Copy

Sample Output

Copy

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