Little Artem and Random Variable

题意翻译

你有两个骰子，第一个骰子的数为 $x$ 的概率是 $a_x$，第二个骰子的数为 $x$ 的概率为 $b_x$，骰子的数字从 $1$ 到 $n$，设第一个骰子的数为 $a$，第二个骰子的数为 $b$。$p1_i$ 表示 $\max(a,b)=i$ 的几率，$p2_i$ 表示 $\min(a,b)=i$ 的几率。告诉你 $p1,p2$，求出序列 $a,b$。 翻译 by @[pigstd](https://www.luogu.com.cn/user/141179)。

题目描述

Little Artyom decided to study probability theory. He found a book with a lot of nice exercises and now wants you to help him with one of them. Consider two dices. When thrown each dice shows some integer from $ 1 $ to $ n $ inclusive. For each dice the probability of each outcome is given (of course, their sum is $ 1 $ ), and different dices may have different probability distributions. We throw both dices simultaneously and then calculate values $ max(a,b) $ and $ min(a,b) $ , where $ a $ is equal to the outcome of the first dice, while $ b $ is equal to the outcome of the second dice. You don't know the probability distributions for particular values on each dice, but you know the probability distributions for $ max(a,b) $ and $ min(a,b) $ . That is, for each $ x $ from $ 1 $ to $ n $ you know the probability that $ max(a,b) $ would be equal to $ x $ and the probability that $ min(a,b) $ would be equal to $ x $ . Find any valid probability distribution for values on the dices. It's guaranteed that the input data is consistent, that is, at least one solution exists.

输入输出格式

输入格式

First line contains the integer $ n $ ( $ 1<=n<=100000 $ ) — the number of different values for both dices. Second line contains an array consisting of $ n $ real values with up to 8 digits after the decimal point — probability distribution for $ max(a,b) $ , the $ i $ -th of these values equals to the probability that $ max(a,b)=i $ . It's guaranteed that the sum of these values for one dice is $ 1 $ . The third line contains the description of the distribution $ min(a,b) $ in the same format.

输出格式

Output two descriptions of the probability distribution for $ a $ on the first line and for $ b $ on the second line. The answer will be considered correct if each value of max( $ a,b $ ) and min( $ a,b $ ) probability distribution values does not differ by more than $ 10^{-6} $ from ones given in input. Also, probabilities should be non-negative and their sums should differ from $ 1 $ by no more than $ 10^{-6} $ .

输入输出样例

输入样例 #1

2
0.25 0.75
0.75 0.25

输出样例 #1

0.5 0.5 
0.5 0.5 

输入样例 #2

3
0.125 0.25 0.625
0.625 0.25 0.125

输出样例 #2

0.25 0.25 0.5 
0.5 0.25 0.25