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;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Text;
using System.Text.RegularExpressions;
using System.Linq;
using System.IO;

class Program
{
    static void Main()
    {
        new Magatro().Solve();
    }
}

class Magatro
{
    private int N, L;
    private int[] A;

    private void Scan()
    {
        var line = Console.ReadLine().Split(' ');
        N = int.Parse(line[0]);
        L = int.Parse(line[1]);
        A = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
    }

    public void Solve()
    {
        Scan();

        for (int i = 1; i < N; i++)
        {

            if (A[i] + A[i - 1] >= L)
            {
                var sb = new StringBuilder();
                sb.AppendLine("Possible");
                for (int j = 1; j < i; j++)
                {
                    sb.AppendLine(j.ToString());
                }

                for (int j = N - 1; j >= i; j--)
                {
                    sb.AppendLine(j.ToString());
                }
                Console.Write(sb.ToString());
                return;
            }
        }
        Console.WriteLine("Impossible");
    }
}