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: Time Limit Exceeded)

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

namespace ConsoleApplication1
{
    class Program
    {
        static long[] dx = new long[] { -1, 0, 1, 0 };
        static long[] dy = new long[] { 0, 1, 0, -1 };

        static int n;
        static int l;
        static List<int> a;

        static void Main(string[] args)
        {
            var str = Console.ReadLine().Split();
            n = Int32.Parse(str[0]);
            l = Int32.Parse(str[1]);
            str = Console.ReadLine().Split();
            a = new List<int>(str.Select(s => Int32.Parse(s)));

            var hist = new Stack<int>();
            List<int> ret = null;
            Solve(hist, 0, n - 1, a.Sum(), ref ret);

            if (ret == null)
            {
                Console.WriteLine("Impossible");
            }
            else
            {
                Console.WriteLine("Possible");
                foreach (var r in ret)
                    Console.WriteLine(r + 1);
            }
        }

        static HashSet<Tuple<int, int>> memo = new HashSet<Tuple<int, int>>();
        static void Solve(Stack<int> hist, int left, int right, int curLen, ref List<int> ret)
        {
            if (ret != null) return;
            var key = new Tuple<int, int>(left, right);
            
            if (memo.Contains(key)) return;
            memo.Add(key);

            if (left == right)
            {
                ret = hist.ToList();
                ret.Reverse();
                return;
            }

            if (curLen >= l)
            {
                hist.Push(left);
                Solve(hist, left + 1, right, curLen - a[left], ref ret);
                hist.Pop();

                hist.Push(right - 1);
                Solve(hist, left, right - 1, curLen - a[right], ref ret);
                hist.Pop();
            }
        }
    }
}