Problem Statement

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:

• Walking over a distance of $d$ costs water of volume $d$ from the hump. A walk that leads to a negative amount of stored water cannot be done.
• Let $v$ be the amount of water stored at the moment. When $v>0$, Camel can jump to any point on the line of his choice. After this move, the volume of the hump becomes $v/2$ (rounded down to the nearest integer), and the amount of stored water becomes $0$.

For each of the oases, determine whether it is possible to start from that oasis and visit all the oases.

Constraints

• $2 ≤ N,V ≤ 2 × 10^5$
• $-10^9 ≤ x_1 < x_2 < ... < x_N ≤ 10^9$
• $V$ and $x_i$ are all integers.

Input

Input is given from Standard Input in the following format:

N V
x_1 x_2 ... x_{N}

Output

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.