Fight the Monster

题意翻译

一个怪物正在攻击Cyberland！ # 杨师傅，一个勇敢的人，要打败怪物。杨师傅和怪物各有3个属性：生命值（HP），攻击力（ATK）和防御力（DEF）。 # 在战斗中，怪物的HP每秒减少$max( 0,ATK_Y−DEF_M )$,杨师傅的HP每秒减少$max( 0,ATK_M−DEF_Y )$。 如果在某个时刻杨师傅的$HP>0$且怪物的$HP\le0 $,杨师傅获胜。 # 杨师傅可以从魔法商店购买属性，每1点HP要h比特币，每1点ATK要a比特币，以及每1点DEF要d比特币。 问杨师傅至少花多少比特币才能战胜怪兽。

题目描述

A monster is attacking the Cyberland! Master Yang, a braver, is going to beat the monster. Yang and the monster each have 3 attributes: hitpoints ( $ HP $ ), offensive power ( $ ATK $ ) and defensive power ( $ DEF $ ). During the battle, every second the monster's HP decrease by $ max(0,ATK_{Y}-DEF_{M}) $ , while Yang's HP decreases by $ max(0,ATK_{M}-DEF_{Y}) $ , where index $ Y $ denotes Master Yang and index $ M $ denotes monster. Both decreases happen simultaneously Once monster's $ HP<=0 $ and the same time Master Yang's $ HP>0 $ , Master Yang wins. Master Yang can buy attributes from the magic shop of Cyberland: $ h $ bitcoins per $ HP $ , $ a $ bitcoins per $ ATK $ , and $ d $ bitcoins per $ DEF $ . Now Master Yang wants to know the minimum number of bitcoins he can spend in order to win.

输入输出格式

输入格式

A monster is attacking the Cyberland! Master Yang, a braver, is going to beat the monster. Yang and the monster each have 3 attributes: hitpoints ( $ HP $ ), offensive power ( $ ATK $ ) and defensive power ( $ DEF $ ). During the battle, every second the monster's HP decrease by $ max(0,ATK_{Y}-DEF_{M}) $ , while Yang's HP decreases by $ max(0,ATK_{M}-DEF_{Y}) $ , where index $ Y $ denotes Master Yang and index $ M $ denotes monster. Both decreases happen simultaneously Once monster's $ HP<=0 $ and the same time Master Yang's $ HP>0 $ , Master Yang wins. Master Yang can buy attributes from the magic shop of Cyberland: $ h $ bitcoins per $ HP $ , $ a $ bitcoins per $ ATK $ , and $ d $ bitcoins per $ DEF $ . Now Master Yang wants to know the minimum number of bitcoins he can spend in order to win.

输出格式

The only output line should contain an integer, denoting the minimum bitcoins Master Yang should spend in order to win.

输入输出样例

输入样例 #1

1 2 1
1 100 1
1 100 100

输出样例 #1

99

输入样例 #2

100 100 100
1 1 1
1 1 1

输出样例 #2

0

说明

For the first sample, prices for $ ATK $ and $ DEF $ are extremely high. Master Yang can buy $ 99 $ HP, then he can beat the monster with $ 1 $ HP left. For the second sample, Master Yang is strong enough to beat the monster, so he doesn't need to buy anything.