Background

Original link: https://oier.team/problems/J1A.

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Did not see the Pleiades.

Problem Description

There is a flame. At the beginning, its temperature is $0$. Next to the flame there are $n$ pieces of charcoal, and each piece has $k$ energy points.

Let $T_i$ denote the temperature of the flame after burning $i$ pieces of charcoal. Then:

$$T_i = \begin{cases} 0 & i = 0 \\ k+ \dfrac{T_{i-1}}{i} & i \neq 0 \end{cases}$$

What is the maximum temperature the flame can reach?

Input Format

This problem has multiple test cases.

The first line contains a positive integer $T$, the number of test cases.

For each test case, input one line with two positive integers $n, k$.

Output Format

For each test case, output one line with a real number representing the maximum temperature the flame can reach, rounded to $1$ digit after the decimal point.

2
1 6
2 7

6.0
10.5

Hint

Sample Explanation #1

For the first test case, there is $1$ piece of charcoal. Before burning any charcoal, the flame temperature is $0$. After burning $1$ piece of charcoal, the flame temperature is $6$, so the answer is $6.0$. For the second test case, there are $2$ pieces of charcoal. Before burning any charcoal, the flame temperature is $0$. After burning $1$ piece of charcoal, the flame temperature is $7$. After burning $2$ pieces of charcoal, the flame temperature is $10.5$, so the answer is $10.5$.

Constraints

Test Point ID	$T \leq$	$n \leq$	$k \leq$
$1 \sim 2$	$5$	$2$	$10$
$3 \sim 4$		$10^7$	$10^9$
$5$	$10^5$	$10^9$

For $100\%$ of the testdata, $1 \leq T \leq 10^5$ and $1 \leq n, k \leq 10^9$.

Translated by ChatGPT 5