306073: CF1142A. The Beatles
Memory Limit:256 MB
Time Limit:1 S
Judge Style:Text Compare
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Description
The Beatles
题意翻译
有n*k个城市围成一个环 在第1,1+k,1+2k,1+(n-1)k个城市处有金拱门 小A非常喜欢吃金拱门的黄金脆皮鸡和吮指原味鸡 小A喜欢诗和远方,所以他要从S城市开始环球旅行 但是他KFC吃多了,于是忘了从哪里出发 他每次会走L条边,但是,他也忘了L是多少 他只记得出发位置距离最近金拱门的边数 当他重新走回S城旅行就停止了 他想问问你 他在旅行途中最多移动了多少次 他在旅行途中最少移动了多少次 (l<=n*k)题目描述
Recently a Golden Circle of Beetlovers was found in Byteland. It is a circle route going through $ n \cdot k $ cities. The cities are numerated from $ 1 $ to $ n \cdot k $ , the distance between the neighboring cities is exactly $ 1 $ km. Sergey does not like beetles, he loves burgers. Fortunately for him, there are $ n $ fast food restaurants on the circle, they are located in the $ 1 $ -st, the $ (k + 1) $ -st, the $ (2k + 1) $ -st, and so on, the $ ((n-1)k + 1) $ -st cities, i.e. the distance between the neighboring cities with fast food restaurants is $ k $ km. Sergey began his journey at some city $ s $ and traveled along the circle, making stops at cities each $ l $ km ( $ l > 0 $ ), until he stopped in $ s $ once again. Sergey then forgot numbers $ s $ and $ l $ , but he remembers that the distance from the city $ s $ to the nearest fast food restaurant was $ a $ km, and the distance from the city he stopped at after traveling the first $ l $ km from $ s $ to the nearest fast food restaurant was $ b $ km. Sergey always traveled in the same direction along the circle, but when he calculated distances to the restaurants, he considered both directions. Now Sergey is interested in two integers. The first integer $ x $ is the minimum number of stops (excluding the first) Sergey could have done before returning to $ s $ . The second integer $ y $ is the maximum number of stops (excluding the first) Sergey could have done before returning to $ s $ .输入输出格式
输入格式
The first line contains two integers $ n $ and $ k $ ( $ 1 \le n, k \le 100\,000 $ ) — the number of fast food restaurants on the circle and the distance between the neighboring restaurants, respectively. The second line contains two integers $ a $ and $ b $ ( $ 0 \le a, b \le \frac{k}{2} $ ) — the distances to the nearest fast food restaurants from the initial city and from the city Sergey made the first stop at, respectively.
输出格式
Print the two integers $ x $ and $ y $ .
输入输出样例
输入样例 #1
2 3
1 1
输出样例 #1
1 6
输入样例 #2
3 2
0 0
输出样例 #2
1 3
输入样例 #3
1 10
5 3
输出样例 #3
5 5