We have N pieces of ropes, numbered 1 through N. The length of piece i is a_i.
At first, for each i (1≤i≤N-1), piece i and piece i+1 are tied at the ends, forming one long rope with N-1 knots. Snuke will try to untie all of the knots by performing the following operation repeatedly:
Is it possible to untie all of the N-1 knots by properly applying this operation? If the answer is positive, find one possible order to untie the knots.
The input is given from Standard Input in the following format:
N L a_1 a_2 ... a_n
If it is not possible to untie all of the N-1 knots, print Impossible
.
If it is possible to untie all of the knots, print Possible
, then print another N-1 lines that describe a possible order to untie the knots. The j-th of those N-1 lines should contain the index of the knot that is untied in the j-th operation. Here, the index of the knot connecting piece i and piece i+1 is i.
If there is more than one solution, output any.
3 50 30 20 10
Possible 2 1
If the knot 1 is untied first, the knot 2 will become impossible to untie.
2 21 10 10
Impossible
5 50 10 20 30 40 50
Possible 1 2 3 4
Another example of a possible solution is 3, 4, 1, 2.