The old Count von Walken ponders along the fence of his
backyard. The fence has a repeating pattern with poles in the
ground at equal distances. Since von Walken has nothing better
to do, he counts the number of steps he takes between each
pole.
The distance between two consecutive poles turns out not to
be an integer multiple of the length of his steps because
sometimes he takes two steps between the poles, and sometimes
he takes three steps.
Von Walken knows that his steps are always 1 meter long, so
he starts thinking of what the distance between the poles may
be. “It must be more than 2 meters, since I occasionally
can fit 3 steps between the poles, but it must be less than 3
meters, since I sometimes only fit 2 steps in
between.”
Task
Given a list of step counts and a distance $D$, determine whether it is possible
that the distance between two poles is $D$ meters. The poles can be
considered to have width $0$, and each step is strictly between
two poles.
To avoid problems with floating point numbers, the result is
guaranteed to be the same even if any pole is moved up to
$10^{7}$ meters.
Input
The input consists of a line containing the real number
$D$ and an integer
$N$, followed by a line
with the spaceseparated list of integer step counts,
$c_1, c_2, \ldots , c_ N$.
It holds that $2 \leq c_ i, D
\leq 3$ and that $0 \leq N
\leq 10\, 000$.
Output
The program should print “possible” if $D$ meters is a possible distance
between the poles, and “impossible” otherwise.
Sample Input 1 
Sample Output 1 
2.505 4
2 2 3 2

impossible

Sample Input 2 
Sample Output 2 
2.1 4
2 2 3 2

possible
