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.

Input

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.

Output

Print one line denoting the minimum cost to color all the nodes in the tree.

Constraints

• \( 1\le n \le 100000\)
• \( 1 \le r \le 1000\)
• \(0 \le A_i, B_i \le 1000000000\)