Coco the Monkey has three magic communications towers on top of his house that he uses to communicate with aliens. The towers are red, green, and blue in color. The red tower has R red connection points, the green tower has G green connection points and the blue tower has B blue connection points. Two connection points of different colours may be connected together with magic wires. Each connection point can be connected to only one wire, and wires must be connected at both ends.
Coco the Monkey may only communicate with aliens if each connection point is connected to some other connection point. Help Coco the Monkey in his quest to talk to aliens by determining how many magic wires should be connected between each pair of communication towers, or determine that it is impossible!
The only line of input contains 3 integers, R, B and G.
If there is no way to connect all the connection points, output "Impossible" (without quotes).
Otherwise output three space separated integers.
The first integer should represent the number of connections between the red tower and the blue tower.
The second integer should represent the number of connections between the red tower and the green tower.
The third integer should represent the number of connections between the blue tower and the green tower.
If there is more than one valid way, output any.
Subtask 1 (18%): 1 ≤ R, B, G ≤ 100
Subtask 2 (21%): 1 ≤ R, B, G ≤ 5000
Subtask 3 (23%): 1 ≤ R, B, G ≤ 1 000 000
Subtask 4 (38%): 1 ≤ R, B, G ≤ 500 000 000
Subtask 5 (0%): Sample Testcases
3 4 5
1 2 3
The towers should be connected as shown:
1 1 1
There is no way to connect the towers.