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 Java7 (OpenJDK 1.7.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
	void run() {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		long l = sc.nextInt();
		long[] a = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}

		for (int i = 0; i < n - 1; i++) {
			if (l <= a[i] + a[i + 1]) {
				System.out.println("Possible");
				for (int j = 0; j < i; j++) {
					System.out.println((j + 1));
				}
				for (int j = n - 2; i <= j; j--) {
					System.out.println((j + 1));
				}
				return;
			}
		}
		System.out.println("Impossible");
	}

	public static void main(String[] args) {
		new Main().run();
	}
}