Plus and xor#2006

Plus and xor

1 second

64 megabytes

Easy

Bitwise exclusive OR (or bitwise addition modulo two) is a binary operation, which is equivalent to applying logical exclusive OR to each pair of bits at the same positions in the binary representation of the operands. In other words, a binary digit of the result is equal to $1$ if and only if the corresponding bits of the operands are different; if the bits are the same, the result is $0$ in that position.

For example, if $X = 101 = 0110010 1_{2}$ X = 101 = 01100101_2,

$Y = 41 = 0010100 1_{2}$ Y = 41 = 00101001_2,

then $X xor Y = 76 = 0100110 0_{2}$ X \text{ xor } Y = 76 = 01001100_2.

In the Pascal programming language, bitwise exclusive OR is written as "xor", and in C/C++ as the symbol "^".

Given two non-negative integers $A$ and $B$ , find two non-negative integers $X$ and $Y$ such that:

$A = X + Y$ A = X + Y
$B = X xor Y$ B = X \text{ xor } Y, where xor is the bitwise exclusive OR operator.
$X$ is the smallest among all numbers for which the conditions $1$ and $2$ are satisfied.

Input

The first line contains the integer $A$ , and the second line contains the integer $B$ ( $0 \leq A, B \leq 2^{64} - 1$ 0 \leq A, B \leq 2^{64} - 1).

Output

Print in one line two non-negative integers $X$ and $Y$ , or print only -1 if no such pair exists.

Examples

Example 1

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Example 10

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X = 101 = 0110010 1_{2}

Y = 41 = 0010100 1_{2}

X xor Y = 76 = 0100110 0_{2}

A = X + Y

B = X xor Y

0 \leq A, B \leq 2^{64} - 1