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William really likes puzzle kits. For one of his birthdays, his friends gifted him a complete undirected edge-weighted graph consisting of nn vertices.

He wants to build a spanning tree of this graph, such that for the first kk vertices the following condition is satisfied: the degree of a vertex with index ii does not exceed didi. Vertices from k+1k+1 to nn 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 nn 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.

Input DIY Tree solution codeforces

The first line of input contains two integers nnkk (2n502≤n≤501kmin(n1,5)1≤k≤min(n−1,5)).

The second line contains kk integers d1,d2,,dkd1,d2,…,dk (1din1≤di≤n).

The ii-th of the next n 1n−1 lines contains nin−i integers wi,i+1,wi,i+2,,wi,nwi,i+1,wi,i+2,…,wi,n (1wi,j1001≤wi,j≤100): weights of edges (i,i+1),(i,i+2),,(i,n)(i,i+1),(i,i+2),…,(i,n).

Output DIY Tree solution codeforces

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

Example
input

Copy DIY Tree solution codeforces
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

output

Copy DIY Tree solution codeforces
95

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