You are given two integers $$$n$$$ and $$$k$$$; $$$k$$$ is an odd number not less than $$$3$$$. Your task is to turn $$$n$$$ into $$$0$$$.

To do this, you can perform the following operation any number of times: choose a number $$$x$$$ from $$$1$$$ to $$$k$$$ and subtract it from $$$n$$$. However, if the current value of $$$n$$$ is even (divisible by $$$2$$$), then $$$x$$$ must also be even, and if the current value of $$$n$$$ is odd (not divisible by $$$2$$$), then $$$x$$$ must be odd.

In different operations, you can choose the same values of $$$x$$$, but you don't have to. So, there are no limitations on using the same value of $$$x$$$.

Calculate the minimum number of operations required to turn $$$n$$$ into $$$0$$$.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10000$$$) — the number of test cases.

Each test case consists of one line containing two integers $$$n$$$ and $$$k$$$ ($$$3 \le k \le n \le 10^9$$$, $$$k$$$ is odd).

Output

For each test case, output one integer — the minimum number of operations required to turn $$$n$$$ into $$$0$$$.

Note

In the first example from the statement, you can first subtract $$$5$$$ from $$$39$$$ to get $$$34$$$. Then subtract $$$6$$$ five times to get $$$4$$$. Finally, subtract $$$4$$$ to get $$$0$$$.

In the second example, you can subtract $$$3$$$ once, and then subtract $$$2$$$ three times.

In the third example, you can subtract $$$2$$$ three times.

To Zero

Examples