
Problem StatementWe 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:
Choose a (connected) rope with a total length of at least L, then untie one of its knots.
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.
Constraints
2≤N≤10^5
1≤L≤10^9
1≤a_i≤10^9
All input values are integers.
InputThe input is given from Standard Input in the following format:
N L
a_1 a_2 ... a_n
OutputIf 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.
Sample Input 13 50
30 20 10
Sample Output 1Possible
2
1
If the knot 1 is untied first, the knot 2 will become impossible to untie.
Sample Input 22 21
10 10
Sample Output 2Impossible
Sample Input 35 50
10 20 30 40 50
Sample Output 3Possible
1
2
3
4
Another example of a possible solution is 3, 4, 1, 2.
