2841: Fight the Monster
Description
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,ATKY-DEFM), while Yang's HP decreases by max(0,ATKM-DEFY), 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.
The first line contains three integers HPY,ATKY,DEFY, separated by a space, denoting the initial HP, ATK and DEF of Master Yang.
The second line contains three integers HPM,ATKM,DEFM, separated by a space, denoting the HP, ATK and DEF of the monster.
The third line contains three integers h,a,d, separated by a space, denoting the price of 1HP, 1ATK and 1DEF.
All numbers in input are integer and lie between 1 and 100 inclusively.
The only output line should contain an integer, denoting the minimum bitcoins Master Yang should spend in order to win.
1 2 1
1 100 1
1 100 100
99
100 100 100
1 1 1
1 1 1
0
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.