Note: This is an approximate problem. There is no exact solution. You must find the most optimal solution. Please, take a look at the sample explanation to ensure that you understand the problem correctly.

Problem statement​

You are given an array A of N elements and two integers L and R. 

Choose an array B which is a permutation of array [1, 2, 3, …., N - 1, N] and build an array C as C[i] = A[B[i]].

The goal is to maximize the value of array function Z

$Z = \sum_\limits{i = L}^{R}\sum_\limits{j = i}^{R}\sum_\limits{k = i}^{j} C[k] \oplus k \oplus (i + j)$ , $\oplus$ represents bitwise-xor operator.

Input

• First line contains three space separated integers N L R.
• Next line contains N space separated integers denoting the value array A. 

Output

• Print N space separated integers denoting the array B

Constraints

$1 \leq N \le 10^3 \\ 1 \le L \le R \le N \\ 1 \le A[i] \le 10^4$

Verdit and Scoring

• Z is the score for each test case.
• If the output is wrong or array B is not a correct permutation, then you will receive a Wrong Answer verdict.