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

\(Z = \lfloor \frac { \sum_\limits{i = L}^{R}\sum_\limits{j = i}^{R}\sum_\limits{k = i}^{j} C[k] } {1 + \sum_\limits{i=L}^{R}\sum_\limits{j=i}^{R}(C[i] \wedge C[j])} \rfloor \times 10^3\) , \(\wedge\) 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

\(N = 10^4 \\ 1 \le L \le R \le N \\ 1 \le A[i] \le 10^6\)

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.