Score: $400$ points

问题陈述

给定非负整数 $a$、$b$ 和 $C$。确定是否存在一对非负整数 $(X, Y)$ 满足以下五个条件。如果存在这样的一对，打印出来。

• $0 \leq X < 2^{60}$
• $0 \leq Y < 2^{60}$
• $\operatorname{popcount}(X) = a$
• $\operatorname{popcount}(Y) = b$
• $X \oplus Y = C$

这里，$\oplus$ 表示按位异或。

如果多个一对 $(X, Y)$ 满足条件，你可以打印出其中任意一个。

什么是popcount？

对于非负整数 $x$，$x$ 的popcount是其二进制表示中1的个数。更精确地说，对于非负整数 $x$，使得 $\displaystyle x=\sum _ {i=0} ^ \infty b _ i2 ^ i\ (b _ i\in\lbrace0,1\rbrace)$，我们有 $\displaystyle\operatorname{popcount}(x)=\sum _ {i=0} ^ \infty b _ i$。

例如，二进制表示中 $13$ 是 1101，所以 $\operatorname{popcount}(13)=3$。什么是按位异或？

对于非负整数 $x, y$，按位异或 $x \oplus y$ 定义如下。

• 二进制表示中 $x \oplus y$ 的 $2^k$ 的位置 $\ (k\geq0)$ 如果 $x$ 和 $y$ 的二进制表示中 $2^k$ 的位置 $\ (k\geq0)$ 只有一个是1，则为1，否则为0。

例如，二进制表示中 $9$ 和 $3$ 分别是 1001 和 0011，所以 $9 \oplus 3 = 10$（二进制表示为 1010）。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given non-negative integers $a$, $b$, and $C$. Determine if there is a pair of non-negative integers $(X, Y)$ that satisfies all of the following five conditions. If such a pair exists, print one.

• $0 \leq X < 2^{60}$
• $0 \leq Y < 2^{60}$
• $\operatorname{popcount}(X) = a$
• $\operatorname{popcount}(Y) = b$
• $X \oplus Y = C$

Here, $\oplus$ denotes the bitwise XOR.

If multiple pairs $(X, Y)$ satisfy the conditions, you may print any of them.

What is popcount?

For a non-negative integer $x$, the popcount of $x$ is the number of $1$s in the binary representation of $x$. More precisely, for a non-negative integer $x$ such that $\displaystyle x=\sum _ {i=0} ^ \infty b _ i2 ^ i\ (b _ i\in\lbrace0,1\rbrace)$, we have $\displaystyle\operatorname{popcount}(x)=\sum _ {i=0} ^ \infty b _ i$.

For example, $13$ in binary is 1101, so $\operatorname{popcount}(13)=3$. What is bitwise XOR?

For non-negative integers $x, y$, the bitwise exclusive OR $x \oplus y$ is defined as follows.

• The $2^k$'s place $\ (k\geq0)$ in the binary representation of $x \oplus y$ is $1$ if exactly one of the $2^k$'s places $\ (k\geq0)$ in the binary representations of $x$ and $y$ is $1$, and $0$ otherwise.

For example, $9$ and $3$ in binary are 1001 and 0011, respectively, so $9 \oplus 3 = 10$ (in binary, 1010).

Constraints

• $0 \leq a \leq 60$
• $0 \leq b \leq 60$
• $0 \leq C < 2^{60}$
• All input values are integers.

Input

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

$a$ $b$ $C$

Output

If there is a pair of non-negative integers that satisfies the conditions, choose one such pair $(X, Y)$ and print $X$ and $Y$ in this order, with a space in between. If no such pair exists, print -1.

Sample Input 1

3 4 7

Sample Output 1

28 27

The pair $(X, Y) = (28, 27)$ satisfies the conditions. Here, $X$ and $Y$ in binary are 11100 and 11011, respectively.

• $X$ in binary is 11100, so $\operatorname{popcount}(X) = 3$.
• $Y$ in binary is 11011, so $\operatorname{popcount}(Y) = 4$.
• $X \oplus Y$ in binary is 00111, so $X \oplus Y = 7$.

If multiple pairs of non-negative integers satisfy the conditions, you may print any of them, so printing 42 45, for example, would also be accepted.

Sample Input 2

34 56 998244353

Sample Output 2

-1

No pair of non-negative integers satisfies the conditions.

Sample Input 3

39 47 530423800524412070

Sample Output 3

540431255696862041 10008854347644927

Note that the values to be printed may not fit in $32$-bit integers.