Problem Statement

For a sequence of non-negative integers $(a _ 1,a _ 2,\ldots,a _ n)$, let us define its $\operatorname{xor}$ as the integer $X$ such that, for all non-negative integer $j$:

• the $2^j$s place of $X$ is $1$ if and only if there is an odd number of elements among $a _ 1,\ldots,a _ n$ whose $2^j$s place is $1$.

You are given a sequence of non-negative integers $A=(A _ 1,A _ 2,\ldots,A _ N)$ of length $N$.

Let $\lbrace s _ 1,s _ 2,\ldots,s _ k\rbrace\ (s _ 1\lt s _ 2\lt\cdots\lt s _ k)$ be the set of all non-negative integers that can be the $\operatorname{xor}$ of a not-necessarily-contiguous (possibly empty) subsequence of $A$.

Given integers $L$ and $R$, print $s _ L,s _ {L+1},\ldots,s _ R$ in this order.

Constraints

• $1\leq N\leq2\times10^5$
• $0\leq A _ i\lt2^{60}\ (1\leq i\leq N)$
• $1\leq L\leq R\leq k$
• $R-L\leq2\times10^5$
• All values in the input are integers.

Input

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

N L R
A _ 1 A _ 2 \ldots A _ N

Output

Print $s _ i\ (L\leq i\leq R)$ in ascending order of $i$, separated by spaces.