DIY Tree

题意翻译

给出${n}$个点的无向带权完全图，找出以下条件的最小生成树： 第${i(1\le i\le k)}$个点的度数$\le d_i$ 输出满足条件的生成树的最小权值。

题目描述

William really likes puzzle kits. For one of his birthdays, his friends gifted him a complete undirected edge-weighted graph consisting of $ n $ vertices. He wants to build a spanning tree of this graph, such that for the first $ k $ vertices the following condition is satisfied: the degree of a vertex with index $ i $ does not exceed $ d_i $ . Vertices from $ k + 1 $ to $ n $ may have any degree. William wants you to find the minimum weight of a spanning tree that satisfies all the conditions. A spanning tree is a subset of edges of a graph that forms a tree on all $ n $ vertices of the graph. The weight of a spanning tree is defined as the sum of weights of all the edges included in a spanning tree.

输入输出格式

输入格式

The first line of input contains two integers $ n $ , $ k $ ( $ 2 \leq n \leq 50 $ , $ 1 \leq k \leq min(n - 1, 5) $ ). The second line contains $ k $ integers $ d_1, d_2, \ldots, d_k $ ( $ 1 \leq d_i \leq n $ ). The $ i $ -th of the next $ n - 1 $ lines contains $ n - i $ integers $ w_{i,i+1}, w_{i,i+2}, \ldots, w_{i,n} $ ( $ 1 \leq w_{i,j} \leq 100 $ ): weights of edges $ (i,i+1),(i,i+2),\ldots,(i,n) $ .

输出格式

Print one integer: the minimum weight of a spanning tree under given degree constraints for the first $ k $ vertices.

输入输出样例

输入样例 #1

10 5
5 3 4 2 1
29 49 33 12 55 15 32 62 37
61 26 15 58 15 22 8 58
37 16 9 39 20 14 58
10 15 40 3 19 55
53 13 37 44 52
23 59 58 4
69 80 29
89 28
48

输出样例 #1

95