Three swimmers

题意翻译

#### 题目描述 三个人在游泳，第 $0$ 分钟这三个人人在游泳池的左侧，之后他们开始来回游，游一个来回分别需要 $a,b,c$ 分钟。 你在第 $p$ 分钟到达游泳池的左侧，请问最少经过多少分钟，你看见一个人在游泳池的左侧？ #### 输入格式 本题多测。第一行一个 $t$ 表示数据组数。 接下来 $t$ 行，每行四个整数 $p,a,b,c$。 #### 输出格式 $t$ 行，每行一个整数表示答案。 #### 数据范围 $1\le t \le1000$，$1\le p,a,b,c\le10^{18}$。

题目描述

Three swimmers decided to organize a party in the swimming pool! At noon, they started to swim from the left side of the pool. It takes the first swimmer exactly $ a $ minutes to swim across the entire pool and come back, exactly $ b $ minutes for the second swimmer and $ c $ minutes for the third. Hence, the first swimmer will be on the left side of the pool after $ 0 $ , $ a $ , $ 2a $ , $ 3a $ , ... minutes after the start time, the second one will be at $ 0 $ , $ b $ , $ 2b $ , $ 3b $ , ... minutes, and the third one will be on the left side of the pool after $ 0 $ , $ c $ , $ 2c $ , $ 3c $ , ... minutes. You came to the left side of the pool exactly $ p $ minutes after they started swimming. Determine how long you have to wait before one of the swimmers arrives at the left side of the pool.

输入输出格式

输入格式

The first line of the input contains a single integer $ t $ ( $ 1 \leq t \leq 1000 $ ) — the number of test cases. Next $ t $ lines contains test case descriptions, one per line. Each line contains four integers $ p $ , $ a $ , $ b $ and $ c $ ( $ 1 \leq p, a, b, c \leq 10^{18} $ ), time in minutes after the start, when you came to the pool and times in minutes it take the swimmers to cross the entire pool and come back.

输出格式

For each test case, output one integer — how long you have to wait (in minutes) before one of the swimmers arrives at the left side of the pool.

输入输出样例

输入样例 #1

4
9 5 4 8
2 6 10 9
10 2 5 10
10 9 9 9

输出样例 #1

1
4
0
8

说明

In the first test case, the first swimmer is on the left side in $ 0, 5, 10, 15, \ldots $ minutes after the start time, the second swimmer is on the left side in $ 0, 4, 8, 12, \ldots $ minutes after the start time, and the third swimmer is on the left side in $ 0, 8, 16, 24, \ldots $ minutes after the start time. You arrived at the pool in $ 9 $ minutes after the start time and in a minute you will meet the first swimmer on the left side. In the second test case, the first swimmer is on the left side in $ 0, 6, 12, 18, \ldots $ minutes after the start time, the second swimmer is on the left side in $ 0, 10, 20, 30, \ldots $ minutes after the start time, and the third swimmer is on the left side in $ 0, 9, 18, 27, \ldots $ minutes after the start time. You arrived at the pool $ 2 $ minutes after the start time and after $ 4 $ minutes meet the first swimmer on the left side. In the third test case, you came to the pool $ 10 $ minutes after the start time. At the same time, all three swimmers are on the left side. A rare stroke of luck! In the fourth test case, all swimmers are located on the left side in $ 0, 9, 18, 27, \ldots $ minutes after the start time. You arrived at the pool $ 10 $ minutes after the start time and after $ 8 $ minutes meet all three swimmers on the left side.