You are given a tree with $$n$$ nodes. You are required to color the tree with $$r$$ colors. Cost of coloring a node with color $$i$$ is $$A_i$$. Also, for each edge, such that the nodes at its end point are colored with the same color $$i$$, there is an additional cost of $$B_i$$. You are required to find the minimum cost to color all the nodes of the tree.
The first line of the input contains 2 integers $$n$$, number of nodes in the tree and $$r$$, number of colors.
The second line of the input contains $$r$$ integers deonting the sequence $$A$$.
The third line of the input contains $$r$$ integers deonting the sequence $$B$$.
Each of the next $$n-1$$ lines conatins two integers $$u$$ and $$v$$ denoting the two nodes which are connected by an edge.
Print one line denoting the minimum cost to color all the nodes in the tree.
Color vertex 1 with color 2 (cost = 3)
Color vertices 2 & 3 with color 1 (cost = 2 each).
No additional cost because there is no edge such that both its end points are colored with same color.
Total cost = 3 + 2 + 2 = 7.