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.

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

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

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

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

0 2 4 6 17 19 21 23

There are 14 not-necessarily-contiguous subsequences of A: (),(2),(17),(21),(2,17),(2,21),(17,21),(21,17),(21,21),(2,17,21),(2,21,17),(2,21,21),(21,17,21), and (2,21,17,21), whose xor⁡xors are as follows.

• The xor⁡xor of () is 0.
• The xor⁡xor of (2) is 2.
• The xor⁡xor of (17) is 17.
• The xor⁡xor of (21) is 21.
• The xor⁡xor of (2,17) is 19.
• The xor⁡xor of (2,21) is 23.
• The xor⁡xor of (17,21) is 4.
• The xor⁡xor of (21,17) is 4.
• The xor⁡xor of (21,21) is 0.
• The xor⁡xor of (2,17,21) is 6.
• The xor⁡xor of (2,21,17) is 6.
• The xor⁡xor of (2,21,21) is 2.
• The xor⁡xor of (21,17,21) is 17.
• The xor⁡xor of (2,21,17,21) is 19.

Therefore, the set of all non-negative integers that can be the ⁡xor of a subsequence of A is {0,2,4,6,17,19,21,23}.