CF820A.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 + 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.

米斯特·B 曾收到一份礼物：一本关于外星人的书，他立刻开始阅读。这本书共有 $c$ 页。

第一天，米斯特·B 阅读了 $v_0$ 页；之后他开始逐渐加快阅读速度。从第二天起，他每天比前一天多读 $a$ 页（即：第一天读 $v_0$ 页，第二天读 $v_0 + a$ 页，第三天读 $v_0 + 2a$ 页，依此类推）。但米斯特·B 毕竟只是人类，因此他每天实际最多只能读 $v_1$ 页。

此外，为了巩固记忆，从第二天起，米斯特·B 每天都必须重读前一天最后 $l$ 页的内容。米斯特·B 在首次读到该书最后一页时，即视为读完此书。

请帮助米斯特·B 计算他读完这本书共需要多少天。

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.

第一行且仅一行包含五个以空格分隔的整数：$c$、$v_0$、$v_1$、$a$ 和 $l$（$1 ≤ c ≤ 1000$，$0 ≤ l < v_0 ≤ v_1 ≤ 1000$，$0 ≤ a ≤ 1000$）——分别表示书的页数、初始阅读速度、最大阅读速度、阅读速度的加速度以及需要重读的页数。

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

输出一个整数——Mister B 读完这本书所需的天数。

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.

在第一个样例测试中，这本书共有 5 页，因此 Mister B 在第一天就读完了整本书。

在第二个样例测试中，Mister B 第一天阅读了第 1–4 页，第二天阅读了第 4–11 页，第三天阅读了第 11–12 页，并读完了整本书。

在第三个样例测试中，Mister B 每天只读 1 页，因此他用了 15 天读完这本书。