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)

use std::io;
use std::collections::VecDeque;

fn main() {
    let mut input = Input::new();
    let n: usize = input.next();
    let l: usize = input.next();
    let a: Vec<usize> = (0..n).map(|_| input.next()).collect();
    let x: Option<usize> = (0..n - 1).filter(|i| a[i + 0] + a[i + 1] >= l).last();
    if x.is_some() {
        println!("Possible");
        let v = x.unwrap() + 1;
        let mut i = 1;
        while i < v {
            println!("{}", i);
            i += 1;
        }
        i = n - 1;
        while i > v {
            println!("{}", i);
            i -= 1;
        }
        println!("{}", v);
    } else {
        println!("Impossible");
    }
}

struct Input {
    queue: VecDeque<String>,
}

impl Input {
    fn new() -> Input {
        Input { queue: VecDeque::new() }
    }

    fn next<T>(&mut self) -> T
        where T: std::str::FromStr,
              T::Err: std::fmt::Debug
    {
        if self.queue.is_empty() {
            let mut line = String::new();
            let _ = io::stdin().read_line(&mut line);
            for x in line.split_whitespace() {
                self.queue.push_back(String::from(x));
            }
        }
        return self.queue.pop_front().unwrap().parse::<T>().unwrap();
    }
}