Mister B and Book Reading

题意翻译

有一本一共 $c$ 页的书，第 $i$ 天可以看 $\min(v_0+a(i-1), v_1)$ 页。但是从第二天开始每一天都必复习前一天读的 $l$ 页。求需要多少天把书看完。 Translated by Eason_AC 2020.11.30

题目描述

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.

输入输出格式

输入格式

First and only line contains five space-separated integers: $ c $ , $ v_{0} $ , $ v_{1} $ , $ a $ and $ l $ ( $ 1<=c<=1000 $ , $ 0<=l&lt;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.

输出格式

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

输入输出样例

输入样例 #1

5 5 10 5 4

输出样例 #1

1

输入样例 #2

12 4 12 4 1

输出样例 #2

3

输入样例 #3

15 1 100 0 0

输出样例 #3

15

说明

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.