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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

N, L = gets.split(" ").map(&:to_i)
ropes = []

ropes << gets.split(" ").map(&:to_i)

history = []

i = 0

loop do
  break if ropes.all? { |r| r.size == 1 || r.inject(0, :+) < L }

  rope = ropes[i]
  j = 1

  loop do
    length = rope.inject(0, :+)
    left_length = rope[0...j].inject(0, :+)
    right_length = rope[j...rope.size].inject(0, :+)

    if length >= L && ((j == 1 && right_length >= L) || (left_length >= L && right_length >= L) || (left_length >= L && j == rope.size - 1) || (rope.size == 2))
      ropes.delete(rope)
      ropes << rope[0...j]
      ropes << rope[j...rope.size] if j < rope.size
      history << ropes[0...i].inject(0) { |s, r| s + r.size } + j
      i = 0
      break
    end

    if j > rope.size - 1
      i += 1
      break
    end

    j += 1
  end
end


if ropes.all? { |r| r.size == 1 }
  puts "Possible"
  puts history 
else
  puts "Impossible"
end