Update Files

题意翻译

### 题意简述 有 $n$ 台电脑需要安装更新文件，开始时仅有 $1$ 号电脑有更新文件。 在每一个小时内，已安装文件的电脑可以通过一条电缆把文件传给另一个未安装文件的电脑。你只有 $k$ 条电缆，也就是说每个小时至多只能有 $k$ 台电脑进行传输。 问所有电脑都接受到更新文件需要多少小时。 ### 输入格式 多组数据，第一行一个整数 $T\ (1\le T\le 10^5)$。 接下来 $T$ 行，每行两个整数 $n,k\ (1\le n\le k\le 10^{18})$。 ### 输出格式 对于每组数据，输出一个整数表示答案。

题目描述

Berland State University has received a new update for the operating system. Initially it is installed only on the $ 1 $ -st computer. Update files should be copied to all $ n $ computers. The computers are not connected to the internet, so the only way to transfer update files from one computer to another is to copy them using a patch cable (a cable connecting two computers directly). Only one patch cable can be connected to a computer at a time. Thus, from any computer where the update files are installed, they can be copied to some other computer in exactly one hour. Your task is to find the minimum number of hours required to copy the update files to all $ n $ computers if there are only $ k $ patch cables in Berland State University.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^5 $ ) — the number of test cases. Each test case consists of a single line that contains two integers $ n $ and $ k $ ( $ 1 \le k \le n \le 10^{18} $ ) — the number of computers and the number of patch cables.

输出格式

For each test case print one integer — the minimum number of hours required to copy the update files to all $ n $ computers.

输入输出样例

输入样例 #1

4
8 3
6 6
7 1
1 1

输出样例 #1

4
3
6
0

说明

Let's consider the test cases of the example: - $ n=8 $ , $ k=3 $ : 1. during the first hour, we copy the update files from the computer $ 1 $ to the computer $ 2 $ ; 2. during the second hour, we copy the update files from the computer $ 1 $ to the computer $ 3 $ , and from the computer $ 2 $ to the computer $ 4 $ ; 3. during the third hour, we copy the update files from the computer $ 1 $ to the computer $ 5 $ , from the computer $ 2 $ to the computer $ 6 $ , and from the computer $ 3 $ to the computer $ 7 $ ; 4. during the fourth hour, we copy the update files from the computer $ 2 $ to the computer $ 8 $ . - $ n=6 $ , $ k=6 $ : 1. during the first hour, we copy the update files from the computer $ 1 $ to the computer $ 2 $ ; 2. during the second hour, we copy the update files from the computer $ 1 $ to the computer $ 3 $ , and from the computer $ 2 $ to the computer $ 4 $ ; 3. during the third hour, we copy the update files from the computer $ 1 $ to the computer $ 5 $ , and from the computer $ 2 $ to the computer $ 6 $ . - $ n=7 $ , $ k=1 $ : 1. during the first hour, we copy the update files from the computer $ 1 $ to the computer $ 2 $ ; 2. during the second hour, we copy the update files from the computer $ 1 $ to the computer $ 3 $ ; 3. during the third hour, we copy the update files from the computer $ 1 $ to the computer $ 4 $ ; 4. during the fourth hour, we copy the update files from the computer $ 4 $ to the computer $ 5 $ ; 5. during the fifth hour, we copy the update files from the computer $ 4 $ to the computer $ 6 $ ; 6. during the sixth hour, we copy the update files from the computer $ 3 $ to the computer $ 7 $ .