The challenge is to keep the lever balanced while adjusting the objects on it. Assume you have a straight, evenly weighted board, 20 meters long and weighing three kilograms. The middle of the board is the center of mass, and we will call that position 0. So the possible positions on the board range from -10 (the left end) to +10 (the right end). The board is supported at positions -1.5 and +1.5 by two equal fulcrums, both two meters tall and standing on a flat floor. On the board are six packages, at positions -8, -4, -3, 2, 5 and 8, having weights of 4, 10, 10, 4, 7 and 8 kilograms, respectively as in the picture below.

Your job is to remove the packages one at a time in such a way that the board rests on both supports without tipping. The board would tip if the net torque around the left fulcrum (resulting from the weights of the packages and the board itself) were counterclockwise or if the net torque around the right fulcrum were clockwise. A possible solution to this problem is: first remove the package at position -4, then the package at 8, then -8, then 5, then -3 and finally 2.

You are to write a program which solves problems like the one described above.

The input contains multiple cases. Each case starts with three integers: the length of the board (in meters, at least 3), the weight of the board (in kilograms) and n the number of packages on the board (n <= 20). The board is supported at positions -1.5 and +1.5 by two equal fulcrums, both two meters tall and standing on a flat floor. The following n lines contain two integers each: the position of a package on board (in meters measured from the center, negative means to the left) and the weight of the package (in kilograms). A line containing three 0's ends the input.

For each case you are to output the number of the case in the format shown below. If there is any solution for a case, output a single line Possible. If there is no solution for a case, output a single line Impossible. There is no solution if in the initial configuration the board is not balanced.

20 3 6 -8 4 -4 10 -3 10 2 4 5 7 8 8 20 3 15 1 10 8 5 -6 8 5 9 -8 4 8 10 -3 10 -4 5 2 9 -2 2 3 3 -3 2 5 1 -6 1 2 5 30 10 2 -8 100 9 91 0 0 0

Case 1: Possible Case 2: Possible Case 3: Impossible

Waterloo local 2001.06.02