Game#409
Petryk and Vasylko are playing a game. The game consists of several rounds; in each round, a coin is tossed. If heads appears, Petryk earns a point; if tails appears, Vasylko earns a point. Points accumulate over rounds, and the first player to reach points wins.
Suddenly, in the middle of the game, the boys have to stop playing. Help Petryk and Vasylko fairly divide the coins at stake, according to the chances each of them had of winning at the moment the game was paused.
The first line contains the number of test cases.
Each test case consists of a single line with four integers , K_1, K_2, and , separated by spaces. is the number of points required to win. K_1 and K_2 are the current points of Petryk and Vasylko, respectively. is the number of coins at stake to be divided between the players.
1 \leq N \leq 50, 0 \leq K_1, K_2 < N, 1 < S < 10^{100}.
For each test case, output on a separate line two integers separated by a space: the number of coins Petryk and Vasylko should get, respectively. The sum of these numbers must be exactly equal to .
Example 1