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 mut sc = Scanner::new();
    while let Ok(n) = sc.wrapped() {
        let l : i32 = sc.next();
        let mut a = vec![0; n];
        for i in 0..n {
            a[i] = sc.next();
        }
        let mut ok = false;
        for i in 0..n-1 {
            if a[i+1] + a[i] >= l {
                println!("Possible");
                for j in (i+1..n-1).rev() { println!("{}", j+1) }
                for j in 0..i { println!("{}", j+1) }
                println!("{}", i+1);
                ok = true;
                break;
            }
        }
        if !ok { println!("Impossible"); }
    }
}

// Scanner

#[allow(dead_code)]
struct Scanner {
    token_buffer : Vec<String>,
    index : usize,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner{
        Scanner { token_buffer: vec![], index: 0 }
    }

    fn wrapped<T>(& mut self) -> Result<T,&str> where T: std::str::FromStr {
        let s = try!(self.fetch_token());
        let t = try!(s.parse::<T>().map_err(|_| "Parse error"));
        Ok(t)
    }
    fn next<T>(& mut self) -> T where T: std::str::FromStr {
        self.wrapped::<T>().unwrap()
    }

    fn fetch_token(&mut self) -> Result<&String,&str> {
        while self.index >= self.token_buffer.len() {
            let mut st = String::new();
            while st.trim() == "" {
                match std::io::stdin().read_line(&mut st) {
                    Ok(l) if l > 0 => continue,
                    Ok(_)  => return Err("End of file"),
                    Err(_) => return Err("Failed to read line"),
                }
            }
            self.token_buffer = st.split_whitespace()
                .map(|x| x.to_string())
                .collect();
            self.index = 0;
        }

        self.index += 1;
        Ok(&self.token_buffer[self.index - 1])
    }
}