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

fn main() {
    let mut stdin = io::stdin();
    let mut lines = String::new();
    let _ = stdin.read_to_string(&mut lines);
    let vec = lines.lines().collect::<Vec<&str>>();
    let vec2 = vec[0].split_whitespace().collect::<Vec<&str>>();
    let n :usize = vec2[0].parse().unwrap();
    let l :usize = vec2[1].parse().unwrap();
    let a :Vec<usize> = vec[1].split_whitespace().map(|s| s.parse().unwrap()).collect();

    let mut q :VecDeque<usize> = VecDeque::new();
    let mut b :Vec<(bool,usize,usize)> = Vec::new();
    let mut junjo :Vec<usize> = Vec::new();
    for i in 0..n {
        b.push((true,1,a[i]));
    }
    for i in 0..(n-1) {
        q.push_back(i);
    }
    while let Some(i) = q.pop_front() {
        let (flag, honsuu, nagasa) = b[i];
        if !flag { continue; }
        if i+honsuu >= n { continue; }
        let (_, honsuu2, nagasa2) = b[i+honsuu];
        let nagasa3 = nagasa + nagasa2;
        if nagasa3 < l {
            continue;
        } else {
            junjo.push(i+honsuu);
            b[i] = (true, honsuu+honsuu2, nagasa3);
            b[i+honsuu] = (false, honsuu2, nagasa2);
            q.push_back(i);
            for k in 0..i {
                if b[i-k-1].0 {
                    q.push_back(i-k-1);
                    break;
                }
            }
        }
    }

    if b[0].1 != n {
        println!("Impossible");
    } else {
        println!("Possible");
        while let Some(j) = junjo.pop() {
            println!("{}", j);
        }
    }
}