A11003. Mister B and Book Reading

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 $v_{0}$ 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 — $v_{0}+2a$ 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.

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.

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

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.