Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Aroma's Search

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWith a new body, our idol Aroma White (or should we call her Kaori Minamiya?) begins to uncover her lost past through the OS space.

The space can be considered a 2D plane, with an infinite number of data nodes, indexed from $$$0$$$, with their coordinates defined as follows:

- The coordinates of the $$$0$$$-th node is $$$(x_0, y_0)$$$
- For $$$i > 0$$$, the coordinates of $$$i$$$-th node is $$$(a_x \cdot x_{i-1} + b_x, a_y \cdot y_{i-1} + b_y)$$$

Initially Aroma stands at the point $$$(x_s, y_s)$$$. She can stay in OS space for at most $$$t$$$ seconds, because after this time she has to warp back to the real world. She doesn't need to return to the entry point $$$(x_s, y_s)$$$ to warp home.

While within the OS space, Aroma can do the following actions:

- From the point $$$(x, y)$$$, Aroma can move to one of the following points: $$$(x-1, y)$$$, $$$(x+1, y)$$$, $$$(x, y-1)$$$ or $$$(x, y+1)$$$. This action requires $$$1$$$ second.
- If there is a data node at where Aroma is staying, she can collect it. We can assume this action costs $$$0$$$ seconds. Of course, each data node can be collected at most once.

Aroma wants to collect as many data as possible before warping back. Can you help her in calculating the maximum number of data nodes she could collect within $$$t$$$ seconds?

Input

The first line contains integers $$$x_0$$$, $$$y_0$$$, $$$a_x$$$, $$$a_y$$$, $$$b_x$$$, $$$b_y$$$ ($$$1 \leq x_0, y_0 \leq 10^{16}$$$, $$$2 \leq a_x, a_y \leq 100$$$, $$$0 \leq b_x, b_y \leq 10^{16}$$$), which define the coordinates of the data nodes.

The second line contains integers $$$x_s$$$, $$$y_s$$$, $$$t$$$ ($$$1 \leq x_s, y_s, t \leq 10^{16}$$$) – the initial Aroma's coordinates and the amount of time available.

Output

Print a single integer — the maximum number of data nodes Aroma can collect within $$$t$$$ seconds.

Examples

Input

1 1 2 3 1 0 2 4 20

Output

3

Input

1 1 2 3 1 0 15 27 26

Output

2

Input

1 1 2 3 1 0 2 2 1

Output

0

Note

In all three examples, the coordinates of the first $$$5$$$ data nodes are $$$(1, 1)$$$, $$$(3, 3)$$$, $$$(7, 9)$$$, $$$(15, 27)$$$ and $$$(31, 81)$$$ (remember that nodes are numbered from $$$0$$$).

In the first example, the optimal route to collect $$$3$$$ nodes is as follows:

- Go to the coordinates $$$(3, 3)$$$ and collect the $$$1$$$-st node. This takes $$$|3 - 2| + |3 - 4| = 2$$$ seconds.
- Go to the coordinates $$$(1, 1)$$$ and collect the $$$0$$$-th node. This takes $$$|1 - 3| + |1 - 3| = 4$$$ seconds.
- Go to the coordinates $$$(7, 9)$$$ and collect the $$$2$$$-nd node. This takes $$$|7 - 1| + |9 - 1| = 14$$$ seconds.

In the second example, the optimal route to collect $$$2$$$ nodes is as follows:

- Collect the $$$3$$$-rd node. This requires no seconds.
- Go to the coordinates $$$(7, 9)$$$ and collect the $$$2$$$-th node. This takes $$$|15 - 7| + |27 - 9| = 26$$$ seconds.

In the third example, Aroma can't collect any nodes. She should have taken proper rest instead of rushing into the OS space like that.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/30/2020 07:49:50 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|