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Competitions

# LCA - 2

The hanging tree with n (1n`105`) vertices numbered from 0 to n - 1 is given. Answer m (1m`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.

Time limit 6 seconds
Memory limit 128 MiB
Input example #1
```3 2
0 1
2 1
1 1 0
```
Output example #1
```2
```
Input example #2
```1 2

0 0
1 1 1
```
Output example #2
```0
```