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 $|X_i - A_i| \leq |Y - A_i|$.

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.

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.

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

见题面 Input 部分

见题面 Output 部分