Score : 1000 points
There are N oases on a number line. The coordinate of the i-th oases from the left is x_i.
Camel hopes to visit all these oases. Initially, the volume of the hump on his back is V. When the volume of the hump is v, water of volume at most v can be stored. Water is only supplied at oases. He can get as much water as he can store at a oasis, and the same oasis can be used any number of times.
Camel can travel on the line by either walking or jumping:
For each of the oases, determine whether it is possible to start from that oasis and visit all the oases.
Input is given from Standard Input in the following format:
N V x_1 x_2 ... x_{N}
Print N lines. The i-th line should contain Possible
if it is possible to start from the i-th oasis and visit all the oases, and Impossible
otherwise.
3 2 1 3 6
Possible Possible Possible
It is possible to start from the first oasis and visit all the oases, as follows:
7 2 -10 -4 -2 0 2 4 10
Impossible Possible Possible Possible Possible Possible Impossible
A oasis may be visited any number of times.
16 19 -49 -48 -33 -30 -21 -14 0 15 19 23 44 52 80 81 82 84
Possible Possible Possible Possible Possible Possible Possible Possible Possible Possible Possible Possible Impossible Impossible Impossible Impossible