CF487A Fight the Monster

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

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

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

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.