Samu is playing a shooting game in play station. There are two apples to aim in this shooting game. Hitting first apple will provide her X points and hitting second apple will provide her Y points. And if she misses the apple she chose to hit, she wont get any point.
Now she is having N coins and each shoot will cost her 1 coin and she needs to score at least W points to win the game.
Samu don't like to loose at any cost. At each turn, she has two choices. The choices include:-
- Hitting first apple with probability P1 percent. However, she might miss it with probability (1-P1) percentage.
- Hitting second apple with probability P2 percent. However, she might miss it with probability (1-P2) percentage.
She would like to know what is the maximal expected probability(as a percentage b/w 0 and 100) of winning the shooting game.
Input Format:
First line contains the number of test cases T.
Each test case consists of six space separated integers of the form X Y N W P1 P2 as described in the statement.
Output Format:
For each test case, print the result as described above in a separate line.
Note:
Choosing to hit any apple is entirely her choice. Both are independent events meaning P1 + P2 may/may not exceed 100.
Output must contain 6 digits after decimal.
Constraints:
1 ≤ T ≤ 10
1 ≤ X,Y ≤ 10
1 ≤ N,W ≤ 103
0 ≤ P1,P2 ≤ 100