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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
class Program
{    
    
    public void slove()
    {
        var inputs = Console.ReadLine().Split();
        int n = int.Parse(inputs[0]);
        int l = int.Parse(inputs[1]);
        int[] rope = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int lastIndex;
        try{
            lastIndex = Enumerable.Range(0, n - 1).First(x => rope[x + 1] + rope[x] >= l);
        }
        catch(InvalidOperationException e){
            System.Console.WriteLine("Impossible");
            return;
        }
        int[] result = 
            Enumerable.Range(0, lastIndex)
            .Concat(Enumerable.Range(0, n - 1).Skip(lastIndex + 1).Reverse())
            .Concat(Enumerable.Range(lastIndex, 1))
            .Select(x => x + 1)
            .ToArray();
        System.Console.WriteLine("Possible");
        System.Console.WriteLine(string.Join("\n", result));
    }
    
    static void Main(string[] args)
    {
        new Program().slove();
    }
}