H :: Hitting the target

Time Limit: 1 Second    Memory Limit: 65536 KB

Genius little Ali is in wonderland, where there are all these amazing, fantastic and adventure games! He has played all the trilling games, but he did not enjoy any. Since Ali is genius he loves intellectual games. While he was walking around, suddenly he noticed a nice challenging game and bought a ticket for it. In this game N seesaws are placed in a row and are numbered 1 to N from left to right. Two consecutive seesaws have a distance of 1 meter. Also there is a wooden cell 1 meter to the right of the rightmost seesaw. In this cell there is one million million ... Rials, as the prize of the one who manages to break the cell. The cell has a resistance of K, meaning that to break it, it must be hit with a stone weighting K or more. 

Initially  there  is  a  stone  of  weight  wi  on  the  left  side  of  i‐th  seesaw.  Ali  can  increase  or  decrease  the weights of these stones arbitrary as long as the weight of the stone on each seesaw remains positive. Total cost of these changes is equal to sum of absolute differences of weight changes for all seesaws. 

Rule of the game is that if a stone of weight A drops on a seesaw with a stone of weight B, the seesaw will throw its stone (A‐B) meters to the right (if A < B, the seesaw just does nothing). After all changes are  made,  a  stone  of  weight  Ws  will  drop  on  the  first  (leftmost)  seesaw.  The  goal  of  the  game  is  to change weights of the stones on the seesaws so that wooden cell will be hit with a large enough stone and  breaks.  Ali  not  only  wants  to  win  the  game,  but  he  also  wants  to  do  it  with  minimum  cost  of changes. Help him with this task. 

 

Input

The first line contains an integer T (T ≤ 100), the number of tests. In the first line of each test there will be three integers N, WS, K (1 ≤ N ≤ 1000, 1 ≤ WS, K ≤ 109), the number of seesaws, weight of the first dropping  stone  and  the  resistance  of  the  wooden  cell,  respectively.  The  next  line  will  consist  of  N weights wi (1 ≤ wi ≤ 109).

 

Output

For each test print the minimum cost of stone changes to break the wooden cell. If Ali cannot win the prize anyway, print “Impossible” instead. (Quotes for clarity) 

 

Sample Input

3
5 123 1
130 23 119 20 34
3 2 2
3 2 1
4 80 1
77 82 76 1000

Sample Output

10
Impossible
1
Submit

Source: AUT 2012