Andrei has a huge pile of $n$ apples. He can divide the pile into two smaller piles: if there are $x$ apples in the pile, he will get piles with $\lfloor \frac{x}{2} \rfloor$$^{\text{∗}}$ and $\lceil \frac{x}{2} \rceil$$^{\text{†}}$ apples. This division takes Andrei $1$ minute.

Andrei wants to eat $k$ apples, but he doesn't want to count them at all. That is why he wants to obtain a pile that contains exactly $k$ apples. Determine whether it is possible to achieve this by performing pile divisions. If it is possible, find the minimum possible time for Andrei to obtain a pile with exactly $k$ apples.

$^{\text{∗}}$$\lfloor \frac{x}{2} \rfloor$ — the largest integer $\le \frac{x}{2}$.

$^{\text{†}}$$\lceil \frac{x}{2} \rceil$ — the smallest integer $\ge \frac{x}{2}$.

Input

Each test consists of several test cases. The first line contains a single integer $t$ $(1 \le t \le 10^4)$ — the number of test cases. The following lines describe the test cases.

In the only line of each test case, two integers $n$ and $k$ are given — the number of apples in the huge pile and the number of apples that Andrei wants to obtain in one pile $(1 \le n, k \le 10^9)$.

Output

For each test case, output $-1$ if it is impossible to obtain a pile with exactly $k$ apples. Otherwise, output the minimum possible time required to obtain such a pile.

Note

In the first test case, after the first division, two piles of $5$ apples will be created. If one of them is divided, it will result in piles with $2$ and $3$ apples, so the answer is $2$.

In the second test case, if the pile is divided into two, it will result in piles with $5$ and $6$ apples, so the answer is $1$.

In the third test case, it is only possible to obtain piles with $1$, $2$, $3$, $5$, $6$, $10$, $11$, or $21$ apples, so the answer is $-1$.

Samples

4
10 3
11 5
21 4
1000000000 1

2
1
-1
29