Score : $200$ points

问题描述

你给定一个整数序列 $A=(A_1,A_2,\ldots,A_N)$，其长度为 $N$，以及满足 $L\leq R$ 的整数 $L$ 和 $R$。

对于每个 $i=1,2,\ldots,N$，找出满足以下两个条件的整数 $X_i$。请注意，要找到的整数总是唯一确定的。

• $L\leq X_i \leq R$。
• 对于所有满足 $L \leq Y \leq R$ 的整数 $Y$，都有 $|X_i - A_i| \leq |Y - A_i|$。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given an integer sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$ and integers $L$ and $R$ such that $L\leq R$.

For each $i=1,2,\ldots,N$, find the integer $X_i$ that satisfies both of the following conditions. Note that the integer to be found is always uniquely determined.

• $L\leq X_i \leq R$.
• For every integer $Y$ such that $L \leq Y \leq R$, it holds that $|X_i - A_i| \leq |Y - A_i|$.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq L\leq R \leq 10^9$
• $1\leq A_i\leq 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$ $L$ $R$

$A_1$ $\ldots$ $A_N$

Output

Print $X_i$ for $i=1,2,\ldots,N$, separated by spaces.

Sample Input 1

5 4 7
3 1 4 9 7

Sample Output 1

4 4 4 7 7

For $i=1$:

• $|4-3|=1$
• $|5-3|=2$
• $|6-3|=3$
• $|7-3|=4$

Thus, $X_i = 4$.

Sample Input 2

3 10 10
11 10 9

Sample Output 2

10 10 10

update @ 2024/3/10 01:13:36