Score : 300 points
There is a box containing N balls. The i-th ball has the integer A_i written on it. Snuke can perform the following operation any number of times:
Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.
Input is given from Standard Input in the following format:
N K A_1 A_2 ... A_N
If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print POSSIBLE
; if it is not possible, print IMPOSSIBLE
.
3 7 9 3 4
POSSIBLE
First, take out the two balls 9 and 4, and return them back along with a new ball, abs(9-4)=5.
Next, take out 3 and 5, and return them back along with abs(3-5)=2.
Finally, take out 9 and 2, and return them back along with abs(9-2)=7.
Now we have 7 in the box, and the answer is therefore POSSIBLE
.
3 5 6 9 3
IMPOSSIBLE
No matter what we do, it is not possible to have 5 in the box. The answer is therefore IMPOSSIBLE
.
4 11 11 3 7 15
POSSIBLE
The box already contains 11 before we do anything. The answer is therefore POSSIBLE
.
5 12 10 2 8 6 4
IMPOSSIBLE