r-906 & IA AI - Psychologic Disco

You are given two non-negative integers $a, b$. You can apply two types of operations on $a$ any number of times and in any order:

• $a \gets a + 1$. The cost of this operation is $x$;
• $a \gets a \oplus 1$, where $\oplus$ denotes the bitwise XOR operation. The cost of this operation is $y$.

Now you are asked to make $a = b$. If it's possible, output the minimum cost; otherwise, report it.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The only line of each test case contains four integers $a, b, x, y$ ($1 \le a, b \le 100, 1 \le x, y \le 10^7$) — the two integers given to you and the respective costs of two types of operations.

Output

For each test case, output an integer — the minimum cost to make $a = b$, or $-1$ if it is impossible.

Note

In the first test case, the optimal strategy is to apply $a \gets a + 1$ three times. The total cost is $1+1+1=3$.

In the second test case, the optimal strategy is to apply $a \gets a + 1$, $a \gets a \oplus 1$, $a \gets a + 1$, $a \gets a \oplus 1$ in order. The total cost is $2+1+2+1=6$.

In the fifth test case, it can be proved that there isn't a way to make $a = b$.