Toy Train (Simplified)

题意翻译

**题目描述** Alice 有一辆玩具火车，和 $n$ 个首尾相接的站台（即火车位于第 $i$（$1\le i<n$）站台时可前往第 $i+1$ 个站台；若 $i=n$，则可前往第 $1$ 个站台。 Alice 需要用火车搬运 $m$ 个糖果，第 $i$ 个糖果需要从 $a_i$ 号站台运到 $b_i$ 号站台。火车容量无限，每到一个站台可以装上 $1$ 个糖果，也可以卸下任意多的糖果。 请你求出从每个车站出发，火车至少要经过（不包括起始站）多少个站台将每个糖果运送完毕。 **输入格式** 第一行包含两个整数 $n,m$（$2\le n\le 200$；$1\le m\le 200$），意义如上所示。 接下来 $m$ 行，每行包含两个整数 $a_i,b_i$（$1\le a_i,b_i\le n$；$a_i\neq b_i$），即该糖果的初始站台与要被运往的站台。 **输出格式** 一行 $n$ 个整数，第 $i$ 个整数表示火车从 $i$ 站台出发时将所有糖果运送完毕至少应经过多少站台。

题目描述

This is a simplified version of the task Toy Train. These two versions differ only in the constraints. Hacks for this version are disabled. Alice received a set of Toy Train™ from Bob. It consists of one train and a connected railway network of $ n $ stations, enumerated from $ 1 $ through $ n $ . The train occupies one station at a time and travels around the network of stations in a circular manner. More precisely, the immediate station that the train will visit after station $ i $ is station $ i+1 $ if $ 1 \leq i < n $ or station $ 1 $ if $ i = n $ . It takes the train $ 1 $ second to travel to its next station as described. Bob gave Alice a fun task before he left: to deliver $ m $ candies that are initially at some stations to their independent destinations using the train. The candies are enumerated from $ 1 $ through $ m $ . Candy $ i $ ( $ 1 \leq i \leq m $ ), now at station $ a_i $ , should be delivered to station $ b_i $ ( $ a_i \neq b_i $ ). The blue numbers on the candies correspond to $ b_i $ values. The image corresponds to the $ 1 $ -st example.The train has infinite capacity, and it is possible to load off any number of candies at a station. However, only at most one candy can be loaded from a station onto the train before it leaves the station. You can choose any candy at this station. The time it takes to move the candies is negligible. Now, Alice wonders how much time is needed for the train to deliver all candies. Your task is to find, for each station, the minimum time the train would need to deliver all the candies were it to start from there.

输入输出格式

输入格式

The first line contains two space-separated integers $ n $ and $ m $ ( $ 2 \leq n \leq 100 $ ; $ 1 \leq m \leq 200 $ ) — the number of stations and the number of candies, respectively. The $ i $ -th of the following $ m $ lines contains two space-separated integers $ a_i $ and $ b_i $ ( $ 1 \leq a_i, b_i \leq n $ ; $ a_i \neq b_i $ ) — the station that initially contains candy $ i $ and the destination station of the candy, respectively.

输出格式

In the first and only line, print $ n $ space-separated integers, the $ i $ -th of which is the minimum time, in seconds, the train would need to deliver all the candies were it to start from station $ i $ .

输入输出样例

输入样例 #1

5 7
2 4
5 1
2 3
3 4
4 1
5 3
3 5

输出样例 #1

10 9 10 10 9 

输入样例 #2

2 3
1 2
1 2
1 2

输出样例 #2

5 6 

说明

Consider the second sample. If the train started at station $ 1 $ , the optimal strategy is as follows. 1. Load the first candy onto the train. 2. Proceed to station $ 2 $ . This step takes $ 1 $ second. 3. Deliver the first candy. 4. Proceed to station $ 1 $ . This step takes $ 1 $ second. 5. Load the second candy onto the train. 6. Proceed to station $ 2 $ . This step takes $ 1 $ second. 7. Deliver the second candy. 8. Proceed to station $ 1 $ . This step takes $ 1 $ second. 9. Load the third candy onto the train. 10. Proceed to station $ 2 $ . This step takes $ 1 $ second. 11. Deliver the third candy. Hence, the train needs $ 5 $ seconds to complete the tasks. If the train were to start at station $ 2 $ , however, it would need to move to station $ 1 $ before it could load the first candy, which would take one additional second. Thus, the answer in this scenario is $ 5+1 = 6 $ seconds.