Level up

Level up is the task of all online games. It's very boooooooooring. There is only level up in those games, except level up.
In a online game, there are N heroes numbered id from 1 to N, each begins with level 1 and 0 Experience. They need to kill monsters to get Exp and level up.

There are many waves of monsters, each wave, the heroes with id from li to ri will come to kill monsters and those hero with level k will get ei*k Exp. If one hero's Exp reach Needk then the hero level up to level k immediately.
After some waves, I will query the maximum Exp from li to ri.
Now giving the information of each wave and Needk, please tell me the answer of my query.

The first line is a number T(1<=T<=30), represents the number of case. The next T blocks follow each indicates a case.
The first line of each case contains three integers N(1<=N<=10000), K(2<=K<=10) and QW(1<=QW<=10000)each represent hero number, the MAX level and querys/waves number.
Then a line with K -1 integers, Need2, Need3...Needk.(1 <= Need2 < Need3 < ... < Needk <= 10000).
Then QW lines follow, each line start with 'W' contains three integers li ri ei (1<=li<=ri<=N , 1<=ei<=10000); each line start with 'Q' contains two integers li ri (1<=li<=ri<=N).

For each case, output the number of case in first line.(as shown in the sample output)
For each query, output the maximum Exp from li to ri.
Output a black line after each case.

2
3 3 5
1 2
W 1 1 1
W 1 2 1
Q 1 3
W 1 3 1
Q 1 3

5 5 8
2 10 15 16 
W 5 5 9
W 3 4 5
W 1 1 2
W 2 3 2
Q 3 5
W 1 3 8
Q 1 2
Q 3 5

Case 1:
3
6

Case 2:
9
18
25

Case 1:
At first ,the information of each hero is 0(1),0(1),0(1) [Exp(level)]
After first wave, 1(2),0(1),0(1);
After second wave, 3(3),1(2),0(1);
After third wave, 6(3),3(3),1(2);
Case 2:
The information of each hero finally:
18(5) 18(5) 25(5) 5(2) 9(2)

NotOnlySuccess

2011 Alibaba Programming Contest