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;

namespace AGC002_C___Knot_Puzzle
{
    class Program
    {
        static int[] process;
        static void Main(string[] args)
        {
            if (solver())
            {
                Console.WriteLine("Possible");
                foreach (int i in process) Console.WriteLine(i);
            }
            else Console.WriteLine("Impossible");

        }
        static bool solver()
        {
            var NL = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            var N = NL[0];
            var L = NL[1];
            var A = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            var totalLength = A.Sum();
            process = new int[N - 1];

            var left = 0;
            var right = (int)(N - 1);
            for (int i = 0; i < N - 1; i++)
            {
                if (totalLength < L) return false;
                if (A[left] <= A[right])
                {
                    process[i] = left + 1;
                    totalLength -= A[left];
                    left++;
                }
                else
                {
                    process[i] = right;
                    totalLength -= A[right];
                    right--;
                }
            }
            return true;
        }
    }
}