Farmer Laura has a barn. In her barn, she has two cows,
Monica and Lydia. Monica and Lydia love food, and they are
quite lazy. For most of the day they chill out in the barn,
waiting for Laura to come serve them a nice meal. Farmer Laura
is always very precise about when to serve them food, so Monica
and Lydia know exactly when to expect food, the same time every
day.
This might sound surprising to you but there’s a problem.
Farmer Laura needs your help. She will be replacing some planks
in the floor of the barn, which means that the cows have to be
moved temporarily from their favorite spots. Since the cows are
infinitely lazy, they refuse to walk themselves. Farmer Laura
has rented an excellent tool to resolve this issue – a cow
crane, designed and crafted specifically for the cow’s
comfort.
We visualize the barn as a onedimensional line. The cow
crane starts at time $t =
0$ at position $x =
0$, and it can move one distance unit per second. The
crane can only carry one cow at a time, but it may pick up and
drop off a cow as many times as necessary. Monica’s current
location is at $x = m$,
and Lydia is located at $x =
l$. Monica will be moved to the temporary location at
$x = M$ and Lydia to
$x = L$. Monica and Lydia
always have their daily meal $t_
m$ and $t_ l$
seconds into the day, so the cows had better be in their
respective temporary locations exactly by these times. You may
assume that it takes no time for the crane to pick up or drop
off a cow and that the two cows can be at the same position at
the same time.
Task
Farmer Laura would like to know if she can move the cows so
that both of them are in place at their temporary location no
later than their daily meal occurs.
Input
Input consists of three lines. The first line consists of
two integers $m$ and
$l$, the current positions
of the cows. The second line consists of two integers
$M$ and $L$, the new positions of the cows.
The third line consists of two integers $t_ m$ and $t_ l$, the time at which the two cows
will be served their daily meal. It is guaranteed that
$10^8 \leq m, l, M, L \leq
10^8$ and $1 \leq t_ m, t_
l \leq 10^8$. It is also guaranteed that both cows will
actually move, i.e., $m \not=
M$ and $l \not=
L$.
Output
Output should consist of a single word. Print “possible” if it is possible to move both cows
before they are served their daily meal. Otherwise, print
“impossible”.
Sample Input 1 
Sample Output 1 
1 1
2 2
6 6

possible

Sample Input 2 
Sample Output 2 
1 1
2 2
5 5

impossible

Sample Input 3 
Sample Output 3 
1 1
1 1
3 5

possible

Sample Input 4 
Sample Output 4 
0 1
2 3
6 3

possible
