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.Collections.Generic;
using System.Linq;
using System.Text;

namespace AGC002
{
    public class C
    {
        private void Run()
        {
            var input = Console.ReadLine().Trim().Split();
            var N = int.Parse(input[0]);
            var L = long.Parse(input[1]);
            var A = Console.ReadLine().Trim().Split().Select(long.Parse).ToArray();

            var total = A.Sum();
            var result = new List<long>();

            int left = 0;
            int right = N - 1;
            while (right - left + 1 >= 2)
            {
                if (total < L)
                {
                    result.Clear();
                    break;
                }
                if (A[left] < A[right])
                {
                    result.Add(left);
                    left++;
                }
                else
                {
                    result.Add(right - 1);
                    right--;
                }
            }

            if (result.Count == 0) { Console.WriteLine("Impossible"); }
            else
            {
                Console.WriteLine("Possible");
                foreach (var x in result)
                {
                    Console.WriteLine(x + 1);
                }
            }
        }

        public static void Main()
        {
            var old = Console.Out;
            using (var writer = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false })
            {
                Console.SetOut(writer);
                new C().Run();
                Console.Out.Flush();
                Console.SetOut(old);
            }
        }
    }
}