Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-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

A. Mister B and Book Reading

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMister B once received a gift: it was a book about aliens, which he started read immediately. This book had *c* pages.

At first day Mister B read *v*_{0} pages, but after that he started to speed up. Every day, starting from the second, he read *a* pages more than on the previous day (at first day he read *v*_{0} pages, at second — *v*_{0} + *a* pages, at third — *v*_{0} + 2*a* pages, and so on). But Mister B is just a human, so he physically wasn't able to read more than *v*_{1} pages per day.

Also, to refresh his memory, every day, starting from the second, Mister B had to reread last *l* pages he read on the previous day. Mister B finished the book when he read the last page for the first time.

Help Mister B to calculate how many days he needed to finish the book.

Input

First and only line contains five space-separated integers: *c*, *v*_{0}, *v*_{1}, *a* and *l* (1 ≤ *c* ≤ 1000, 0 ≤ *l* < *v*_{0} ≤ *v*_{1} ≤ 1000, 0 ≤ *a* ≤ 1000) — the length of the book in pages, the initial reading speed, the maximum reading speed, the acceleration in reading speed and the number of pages for rereading.

Output

Print one integer — the number of days Mister B needed to finish the book.

Examples

Input

5 5 10 5 4

Output

1

Input

12 4 12 4 1

Output

3

Input

15 1 100 0 0

Output

15

Note

In the first sample test the book contains 5 pages, so Mister B read it right at the first day.

In the second sample test at first day Mister B read pages number 1 - 4, at second day — 4 - 11, at third day — 11 - 12 and finished the book.

In third sample test every day Mister B read 1 page of the book, so he finished in 15 days.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/18/2018 02:41:41 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|