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.Text;
using System.Threading.Tasks;
using System.Collections;
using System.Diagnostics;

namespace CompetitiveProgramming
{
  class Solve
  {
    public Solve()
    {
      int N = Scanner.nextInt();
      int L = Scanner.nextInt();
      int[] a = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();

      int index = -1;
      for (int i = 0; i < N - 1; i++)
      {
        if (a[i] + a[i + 1] >= L) 
        {
          index = i;
          break;
        }
      }
      if (index == -1)
      {
        Console.WriteLine("Impossible");
        return;  
      }

      Console.WriteLine("Possible");

      for (int i = 0; i < index; i++) 
      {
        Console.WriteLine(i + 1);
      }
      for (int i = N - 2; i > index; i--)
      {
        Console.WriteLine(i + 1);
      }
      Console.WriteLine(index + 1);
    }
  }

  class Program
  {
    static void Main(string[] args)
    {
      new Solve();
    }
  }

  public class Pair<T, U>
  {
    public Pair()
    {

    }
    public Pair(T first, U second)
    {
      this.first = first;
      this.second = second;
    }
    public T first { get; set; }
    public U second { get; set; }
  }

  class Scanner
  {
    private static List<string> buf = new List<string>();

    private static void next()
    {
      if (buf.Count == 0)
      {
        buf = Console.ReadLine().Split().ToList();
      }
    }

    private static string pop()
    {
      string ret = buf[0];
      buf.RemoveAt(0);
      return ret;
    }

    public static int nextInt()
    {
      next();
      return int.Parse(pop());
    }
    public static long nextLong()
    {
      next();
      return long.Parse(pop());
    }
    public static string nextString()
    {
      next();
      return pop();
    }
    public static double nextDouble()
    {
      next();
      return double.Parse(pop());
    }
  }

}