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A traditional game is played between two players on a pool of n numbers (not necessarily distinguishing ones).
The first player will choose from the pool a number x1 lying in [a, b] (0 < a < b), which means a <= x1 <= b. Next the second player should choose a number y1 such that y1 - x1 lies in [a, b] (Attention! This implies y1 > x1 since a > 0). Then the first player should choose a number x2 such that x2 - y1 lies in [a, b]... The game ends when one of them cannot make a choice. Note that a player MUST NOT skip his turn.
A player's score is determined by the numbers he has chose, by the way:
player1score = x1 + x2 + ...
player2score = y1 + y2 + ...
If you are player1, what is the maximum score difference (player1score - player2score) you can get? It is assumed that player2 plays perfectly.
The first line contains a single integer t (1 <= t <= 20) indicating the number of test cases. Then follow the t cases. Each case contains exactly two lines. The first line contains three integers, n, a, b (2 <= n <= 10000, 0 < a < b <= 100); the second line contains n integers, the numbers in the pool, any of which lies in [-9999, 9999].
For each case, print the maximum score difference player1 can get. Note that it can be a negative, which means player1 cannot win if player2 plays perfectly.
3 6 1 2 1 3 -2 5 -3 6 2 1 2 -2 -1 2 1 2 1 0
-3 0 1
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