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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;



int main()
{
	
ll n,L;
cin>>n>>L;
vector<ll>v(n),ans(n-1);
ll sum=0;
for(ll i=0;i<n;i++)
{
	cin>>v[i];
	sum+=v[i];
}

	for(ll f=0,l=n-1,j=0;j<n-1;j++)
	{
		if(v[f]+v[f+1]<v[l]+v[l-1])
		{
			if(sum>=L)
			sum-=v[f];
			else
			{
				cout<<"Impossible";
				return 0;
			}
			ans[j]=f+1;
			f++;
			
			
		}
		else
		{
			if(sum>=L)
			sum-=v[l];
			else
			{
				cout<<"Impossible";
				return 0;
			}
			ans[j]=l;
			l--;
		}
		
	}
	
	cout<<"Possible\n";
	for(auto x:ans)cout<<x<<"\n";
	



}