The hanging tree with n (1 ≤ n ≤ 105) vertices numbered from 0 to n - 1 is given. Answer m (1 ≤ m ≤ 107) queries about Least Common Ancestor for pair of vertices.

The queries are numbered in the next way. Given values a1, a2 and x, y и z. Numbers a3, ..., a2m are generated in the next way:

ai = (x * ai-2 + y * ai-1 + z) mod n.

First query has the form <a1, a2>. If the answer to the (i - 1)-th query is v, then the i-th query has the form <(a2i-1 + v) mod n, a2i>.

Input

First line contains two numbers n and m. The root of the tree has number 0. Second line contains n - 1 integers, i-th of these numbers equals to the parent of the vertex i. Third line contains two integers in the range from 0 to n - 1: a1 and a2. Fourth line contains three integers: x, y and z, they are non-negative and no more than 109.

Output

Print the sum of the vertex numbers - the answers to all queries.