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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
  let (n, l): (i32, i32) = read_tuple();
  let vec: Vec<i32> = read_vec();
  
  let mut knot = None;
  for (w, i) in vec.windows(2).zip(1..) {
    if w[0] + w[1] >= l {
      knot = Some(i);
      break;
    }
  };
  
  let mut ans: Vec<i32> = vec![];
  match knot {
    None => {
      println!("Impossible");
      return
    },
    
    Some(i) => {
      println!("Possible");
      for j in 1 .. i {
        ans.push(j);
      }
      for j in (i .. n).rev() {
        ans.push(j);
      }
      print_vec(&ans, " ");
    }
  }
}

fn read_tuple<T1: std::str::FromStr, T2: std::str::FromStr>() -> (T1, T2) {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  let mut it = buf.trim().split_whitespace();
  let x = it.next().unwrap().parse::<T1>().ok().unwrap();
  let y = it.next().unwrap().parse::<T2>().ok().unwrap();
  (x, y)
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
  let mut buf = String::new();
  std::io::stdin().read_line(&mut buf).ok();
  buf.trim().split_whitespace().map(|t| t.parse::<T>().ok().unwrap()).collect()
}

fn print_vec<T: std::string::ToString>(vec: &Vec<T>, sep: &str) {
  let out = vec.iter().map(|e| e.to_string()).collect::<Vec<_>>().as_slice().join(sep);
  println!("{}", out);
}