Across the River

Time Limit: 10 Seconds    Memory Limit: 32768 KB

n men and m women (1 <= n <= m <= 200) want to cross a river. There is only one boat on the river, and it can carry k (k >= 1) people at most at a time. So they have to design a strategy to cross the river, but the following rule must be obeyed. That is, at any time, either on the riverside or on the boat, there's no woman or the number of women is no less than the number of men. So you task is to design a strategy that take all the people across the river, and this strategy takes the least steps. (take some people from one side to the other side counts one step). If no such strategy exists, just output "Impossible".

Input

The input consists of several test cases, each input consists of three integers n, m, k. The input is terminated by EOF.

Output

For each test case, output the least steps if possible, or "Impossible" if there is no such strategy.

Sample Input

2 2 2
2 2 1

Sample Output

5
Impossible

Submit

Source: ZOJ Monthly, January 2005