Problem F
Freestyle Masonry

An interesting brick layout, photo by Bobo Boom

Figure 1: Visualization of Sample Input $2$. The red bricks have already been placed by Fred. The blue bricks still need to be placed to complete the wall (the only possible design in this case).

Maybe he should have made a plan before starting to build the wall, but now it is too late. Fred only has a bunch of $2\times 1$ bricks left and wants to finish the wall. Can he still complete it with the remaining $2\times 1$ bricks? Note that the wall to be built should have a width of exactly $w$ units and a height of exactly $h$ units.

Input

The input consists of:

• One line with two integers $w$ and $h$ ($1\leq w\leq 2\cdot 10^5$, $1\leq h\leq 10^6$), the width and height of the wall Fred wants to build.

• One line with $w$ integers $h_1,\dots ,h_n$ ($0\leq h_i\leq 10^6$), where $h_i$ is the current height of the wall at position $i$.

Output

Output “possible” if Fred can complete his wall and “impossible” otherwise.

3 3
0 0 1

possible

6 3
1 0 1 1 0 1

possible

6 2
1 0 1 1 0 1

impossible

5 2
1 2 3 2 2

impossible