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.

First and only line contains five space-separated integers: c, v0, v1, a and l (1 \le c \le 1000, 0 \le l \lt v0 \le v1 \le 1000, 0 \le a \le 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.