CF1874B.Jellyfish and Math

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题目描述

Jellyfish is given the non-negative integers $a$ , $b$ , $c$ , $d$ and $m$ . Initially $(x,y)=(a,b)$ . Jellyfish wants to do several operations so that $(x,y)=(c,d)$ .

For each operation, she can do one of the following:

$x := x\,\&\,y$ ,
$x := x\,|\,y$ ,
$y := x \oplus y$ ,
$y := y \oplus m$ .

Here $\&$ denotes the bitwise AND operation, $|$ denotes the bitwise OR operation and $\oplus$ denotes the bitwise XOR operation.

Now Jellyfish asks you for the minimum number of operations such that $(x,y)=(c,d)$ .

输入格式

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \leq t \leq 10^5$ ). The description of the test cases follows.

The only line of each test case contains five integers, $a$ , $b$ , $c$ , $d$ and $m$ ( $0 \leq a, b, c, d, m < 2^{30}$ ).

输出格式

For each test case, output a single integer — the minimum number of operations. If this cannot be achieved, output $-1$ instead.

输入输出样例

输入#1

10
1 0 1 1 1
3 3 1 2 1
1 6 0 7 1
2 4 4 9 8
21 4 0 17 28
50 50 0 0 39
95 33 1 33 110
138 202 174 64 108
78 340 68 340 461
457 291 491 566 766

输出#1

说明/提示

In the first test case, we can do the operation $y = x \oplus y$ .

In the second test case, it is not possible to change $(x,y)=(1,2)$ using any sequence of operations.

In the third test case, we can do the operation $x = x\,\&\,y$ followed by the operation $y = y \oplus m$ .

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