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.ComponentModel;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var nl = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
			int n = (int)nl[0];
			long l = nl[1];
			var a = Console.ReadLine().Split(' ').Select(long.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 < 0) {
				Console.WriteLine("Impossible");
				return;
			}

			var sb = new StringBuilder();
			for (int i = 0; i < index; i++) {
				sb.AppendLine((i + 1).ToString());
			}

			for (int i = n - 1; i >= index + 1; i--) {
				sb.AppendLine(i.ToString());
			}

			Console.WriteLine("Possible");
			Console.Write(sb.ToString());
		}
	}
}