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: Wrong Answer)

    using System;
    using System.Linq;
    using System.Collections.Generic;
    using System.Text.RegularExpressions;
    using System.Text;
     
    public class Program
    {
        public void Proc() {
            Reader.IsDebug = false;
            long[] inpt = Reader.ReadLine().Split(' ').Select(a=>long.Parse(a)).ToArray();

            int itemCount = (int)inpt[0];
            long minLength = inpt[1];

            long[] list = Reader.ReadLine().Split(' ').Select(a=>long.Parse(a)).ToArray();

            for(int i=1; i<list.Length; i++) {
                if(list[i-1]+list[i]>=minLength) {
                    Console.WriteLine("Possible");
                    StringBuilder ans = new StringBuilder();
                    for(int j=0; j<i-1; j++) {
                        ans.AppendLine((j+1).ToString());
                    }
                    for(int j=i; j<list.Length-1; j++) {
                        ans.AppendLine((j+1).ToString());
                    }
                    ans.AppendLine(i.ToString());
                    Console.Write(ans.ToString());
                    return;
                }
            }
            Console.WriteLine("Impossible");
        }



        public class Reader {
            public static bool IsDebug = true;
            private static System.IO.StringReader SReader;
            private static string InitText = @"




2 21
10 10





";
            public static string ReadLine() {
                if(IsDebug) {
                    if(SReader == null) {
                        SReader = new System.IO.StringReader(InitText.Trim());
                    }
                    return SReader.ReadLine();
                } else {
                    return Console.ReadLine();
                }
            }
        }
        public static void Main(string[] args)
        {
            Program prg = new Program();
            prg.Proc();
        }
    }