Problem:
Problem Statement

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:

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.

Input

The input is given from Standard Input in the following format:

N L
a_1 a_2 ... a_n

Output

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.

Sample Input 1

3 50
30 20 10

Sample Output 1

Possible
2
1

If the knot 1 is untied first, the knot 2 will become impossible to untie.

Sample Input 2

2 21
10 10

Sample Output 2

Impossible

Sample Input 3

5 50
10 20 30 40 50

Sample Output 3

Possible
1
2
3
4

Another example of a possible solution is 3, 4, 1, 2.

Solution in OCaml (4.02.3) (judge verdict: Accepted)

module A = Array
module C = Char
module I = Int64
module L = List
module Q = Queue

let pf = Printf.printf
let sf = Scanf.scanf
let ssf = Scanf.sscanf

let read_int () = sf "%d " (fun x -> x)
let read_float () = sf "%f " (fun x -> x)
let read_array read n = A.init n (fun _ -> read ())
let err s = raise (Failure s)

let inf = int_of_float 1e18
let eps = 1e-11

module S = struct
  include String
  let of_array a = String.init (A.length a) (A.get a)
  let to_array s = A.init (String.length s) (String.get s)
end;;

let _ =
  let n = read_int () in
  let len = read_int () in
  let a = read_array read_int n in
  let (max_len, pos) = A.init (n - 1) (fun x -> x) |>
                         A.map (fun i -> (a.(i) + a.(i + 1), i)) |>
                         A.fold_left max (0, 0) in
  if max_len >= len
  then A.append (A.init pos (fun x -> x+1)) (A.init (n-pos-1) (fun x -> n-x-1)) |>
         ( print_endline "Possible";
           A.iter (fun x -> string_of_int x |> print_endline) )
  else print_endline "Impossible"