Mister B and Book Reading

2000ms

262144K

Description:

Mister 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 v₀ 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 v₀ pages, at second — v₀ + a pages, at third — v₀ + 2a pages, and so on). But Mister B is just a human, so he physically wasn't able to read more than v₁ 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, v₀, v₁, a and l (1 ≤ c ≤ 1000, 0 ≤ l < v₀ ≤ v₁ ≤ 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.

Sample Input:

5 5 10 5 4

Sample Output:

Sample Input:

12 4 12 4 1

Sample Output:

Sample Input:

15 1 100 0 0

Sample Output:

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.

Informação

Provedor Codeforces

Código CF820A