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++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
#include <queue>
using namespace std;

int main(){
  int n, L;
  cin >> n >> L;
  vector<long>a(n);
  for(int i=0; i<n; i++)cin >> a[i];
  long s=accumulate(a.begin(), a.end(), 0L);
  queue<int>ret;
  int l=0, r=n-1;
  for(int i=0; i<n-1; i++){
    if(s<L){
      cout << "Impossible";
      return 0;
    }
    if(a[l]<a[r]){
      s-=a[l];
      ret.push(l+1);
      l++;
    }
    else{
      s-=a[r];
      ret.push(r);
      r--;
    }
  }
  cout << "Possible\n";
  while(!ret.empty()){
    cout << ret.front() << endl;
    ret.pop();
  }
  return 0;
}