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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.TreeMap;

public class Main {
	public static void main(String[] args) throws Exception{
		String answerText = "Possible";
		ArrayList<Integer> answerList = new ArrayList<Integer>();
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] array;
		array = br.readLine().split(" ");
		int n = Integer.parseInt(array[0]);//ロープの本数
		int l = Integer.parseInt(array[1]);//長さL
		TreeMap<Integer,Integer> map = new TreeMap<Integer,Integer>();

		int cnt = 0;
		for(String str:br.readLine().split(" ")){
			map.put(cnt, Integer.parseInt(str));
			cnt++;
		}

		int total = getLength(map);

		while(true){
			if(map.size() == 1){
				break;
			}
			if(total >= l){
				int first = map.firstKey();
				int last = map.lastKey();
				if(map.get(first) < map.get(last)){
					total -= map.get(first);
					answerList.add(first+1);
					map.remove(first);
				}else{
					total -= map.get(last);
					answerList.add(last);
					map.remove(last);
				}
			}else{
				answerText = "Impossible";
				break;
			}
		}
		System.out.println(answerText);
		for(Integer i:answerList){
			System.out.println(String.valueOf(i));
		}
	}

	private static Integer getLength(TreeMap<Integer,Integer> map){
		int ret = 0;

		for(int i:map.values()){
			ret += i;
		}
		return ret;
	}
}