# Orange Boy Can You Solve It Out? Ep. 31 (Hard)

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# Childish War (Hard)

Miss. Broken Tail(Wei Duan) is the Math teacher of NFLS Class 8 Junior 3.She is a kind teacher.
Miss. East(Fang Dong) is the Math teacher of NFLS Class 4 Junior 3.She is a kind teacher too.
Tail loves walking around the Xuanwu Lake to relax. So does East.
There are N islands numbered from 1 to N on Xuanwu Lake and there are M bidirectional weighted edges connecting them. It is made sure that the islands are connected and no edge has negative weight.
Tail is located at island S and East is located at island T. They decided to play a childish game.
The game has Q rounds, in each round East chooses an positive integer R and draw a circle centered at her position with the radius R1.
Tail will choose an radius R2 and draw a circle centered at her position with R2 as radius too. The score of Tail will be calculated as follows:
Let's call the number of islands included in Tail's circle but not in East's circle X.Let's call the number of islands included in Tail's circle and in East's circle Y. Then the score of Tail's circle is aX+bY where a and b are given.
For each query, find the max score of Tail's circle.

# Example

Input
graph={
[1,2,2],
[2,3,2],
[1,4,2],
[4,3,2],
[1,3,3],
}
S=1 T=3 a=3 b=1
Query={
,

}
Output
10
4
Explain
Q1:Tail can draw a circle of radius 3 so that X=3(1,2,4) Y=1(3).
Q2:Tail can draw a circle of radius 4 so that X=0 Y=4(1,2,3,4).

# Constriants  