Presents in Bankopolis

题意翻译

给出 $n$ 个点，$m$ 条边的有向图。 求出一条任意起点、途中不能经过之前走过的点，并且包含 $k$ 个点的权值最小的路径，如果不存在就输出 $-1$ 。 边 $(u, v)$经过点 $x$，当且仅当 $min(u,v) < x < max(u,v)$ 。 $1 \leq n,k \leq 80, 0\leq m\leq 2000, 1\leq u_i, v_i \leq n, 1\leq c_i\leq 1000$

题目描述

Bankopolis is an incredible city in which all the $ n $ crossroads are located on a straight line and numbered from $ 1 $ to $ n $ along it. On each crossroad there is a bank office. The crossroads are connected with $ m $ oriented bicycle lanes (the $ i $ -th lane goes from crossroad $ u_{i} $ to crossroad $ v_{i} $ ), the difficulty of each of the lanes is known. Oleg the bank client wants to gift happiness and joy to the bank employees. He wants to visit exactly $ k $ offices, in each of them he wants to gift presents to the employees. The problem is that Oleg don't want to see the reaction on his gifts, so he can't use a bicycle lane which passes near the office in which he has already presented his gifts (formally, the $ i $ -th lane passes near the office on the $ x $ -th crossroad if and only if $ min(u_{i},v_{i})&lt;x&lt;max(u_{i},v_{i}))) $ . Of course, in each of the offices Oleg can present gifts exactly once. Oleg is going to use exactly $ k-1 $ bicycle lane to move between offices. Oleg can start his path from any office and finish it in any office. Oleg wants to choose such a path among possible ones that the total difficulty of the lanes he will use is minimum possible. Find this minimum possible total difficulty.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ ( $ 1<=n,k<=80 $ ) — the number of crossroads (and offices) and the number of offices Oleg wants to visit. The second line contains single integer $ m $ ( $ 0<=m<=2000 $ ) — the number of bicycle lanes in Bankopolis. The next $ m $ lines contain information about the lanes. The $ i $ -th of these lines contains three integers $ u_{i} $ , $ v_{i} $ and $ c_{i} $ ( $ 1<=u_{i},v_{i}<=n $ , $ 1<=c_{i}<=1000 $ ), denoting the crossroads connected by the $ i $ -th road and its difficulty.

输出格式

In the only line print the minimum possible total difficulty of the lanes in a valid path, or -1 if there are no valid paths.

输入输出样例

输入样例 #1

7 4
4
1 6 2
6 2 2
2 4 2
2 7 1

输出样例 #1

6

输入样例 #2

4 3
4
2 1 2
1 3 2
3 4 2
4 1 1

输出样例 #2

3

说明

In the first example Oleg visiting banks by path $ 1→6→2→4 $ . Path $ 1→6→2→7 $ with smaller difficulity is incorrect because crossroad $ 2→7 $ passes near already visited office on the crossroad $ 6 $ . In the second example Oleg can visit banks by path $ 4→1→3 $ .