Floor Number

1000ms

262144K

Description:

Vasya goes to visit his classmate Petya. Vasya knows that Petya's apartment number is $$$n$$$.

There is only one entrance in Petya's house and the distribution of apartments is the following: the first floor contains $$$2$$$ apartments, every other floor contains $$$x$$$ apartments each. Apartments are numbered starting from one, from the first floor. I.e. apartments on the first floor have numbers $$$1$$$ and $$$2$$$, apartments on the second floor have numbers from $$$3$$$ to $$$(x + 2)$$$, apartments on the third floor have numbers from $$$(x + 3)$$$ to $$$(2 \cdot x + 2)$$$, and so on.

Your task is to find the number of floor on which Petya lives. Assume that the house is always high enough to fit at least $$$n$$$ apartments.

You have to answer $$$t$$$ independent test cases.

Input:

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. Then $$$t$$$ test cases follow.

The only line of the test case contains two integers $$$n$$$ and $$$x$$$ ($$$1 \le n, x \le 1000$$$) — the number of Petya's apartment and the number of apartments on each floor of the house except the first one (there are two apartments on the first floor).

Output:

For each test case, print the answer: the number of floor on which Petya lives.

Sample Input:

Sample Output:

Note:

Consider the first test case of the example: the first floor contains apartments with numbers $$$1$$$ and $$$2$$$, the second one contains apartments with numbers $$$3$$$, $$$4$$$ and $$$5$$$, the third one contains apartments with numbers $$$6$$$, $$$7$$$ and $$$8$$$. Therefore, Petya lives on the third floor.

In the second test case of the example, Petya lives in the apartment $$$1$$$ which is on the first floor.

Informação

Provedor Codeforces

Código CF1426A