Problem:
Score : 300 points

Problem Statement

There is a box containing N balls. The i-th ball has the integer A_i written on it.
Snuke can perform the following operation any number of times:

Take out two balls from the box. Then, return them to the box along with a new ball, on which the absolute difference of the integers written on the two balls is written.

Determine whether it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written.

Constraints

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \leq K \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

If it is possible for Snuke to reach the state where the box contains a ball on which the integer K is written, print POSSIBLE; if it is not possible, print IMPOSSIBLE.

Sample Input 1

3 7
9 3 4

Sample Output 1

POSSIBLE

First, take out the two balls 9 and 4, and return them back along with a new ball, abs(9-4)=5.
Next, take out 3 and 5, and return them back along with abs(3-5)=2.
Finally, take out 9 and 2, and return them back along with abs(9-2)=7.
Now we have 7 in the box, and the answer is therefore POSSIBLE.

Sample Input 2

3 5
6 9 3

Sample Output 2

IMPOSSIBLE

No matter what we do, it is not possible to have 5 in the box. The answer is therefore IMPOSSIBLE.

Sample Input 3

4 11
11 3 7 15

Sample Output 3

POSSIBLE

The box already contains 11 before we do anything. The answer is therefore POSSIBLE.

Sample Input 4

5 12
10 2 8 6 4

Sample Output 4

IMPOSSIBLE

Solution in Rust (1.15.1) (judge verdict: Accepted)

//! https://github.com/hatoo/competitive-rust-snippets
//!
//! MIT License
//!
//! Copyright (c) 2018 hatoo
//!
//! Permission is hereby granted, free of charge, to any person obtaining a copy
//! of this software and associated documentation files (the "Software"), to deal
//! in the Software without restriction, including without limitation the rights
//! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
//! copies of the Software, and to permit persons to whom the Software is
//! furnished to do so, subject to the following conditions:
//!
//! The above copyright notice and this permission notice shall be included in all
//! copies or substantial portions of the Software.
//!
//! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
//! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
//! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
//! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
//! SOFTWARE.
#![allow(
    unused_imports,
    unused_attributes,
    unused_macros,
    dead_code,
    non_snake_case
)]
use std::cmp::{max, min, Ordering};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::{stdin, stdout, BufWriter, Write};
use std::iter::FromIterator;
#[macro_export]
macro_rules !get {(@inner [$src :expr ] chars ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .chars () .collect ::<Vec <char >>() } } ;(@inner [$src :expr ] usize1 ) =>{{get !(@inner [$src ] usize ) -1 } } ;(@inner [$src :expr ] [usize1 ] ) =>{{get !(@inner [$src ] [usize ] ) .into_iter () .map (|v |v -1 ) .collect ::<Vec <usize >>() } } ;(@inner [$src :expr ] [[usize1 ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [usize1 ] ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [usize1 ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [usize1 ] ) ) .flatten () .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [[chars ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] chars ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [chars ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] chars ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [($($tt :tt ) ,*) ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] ($($tt ) ,*) ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] ($($tt :tt ) ,*) ) =>{{let mut buf :String =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;let mut iter =buf .split_whitespace () ;($(get !(@inner_elem_parse [$tt ] iter .next () .unwrap () ) ,) *) } } ;(@inner [$src :expr ] [$t :ty ] ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .split_whitespace () .map (|t |t .parse ::<$t >() .unwrap () ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [[$t :ty ] ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [$t ] ) ) .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] [$t :ty ;$n :expr ] ) =>{{(0 ..$n ) .map (|_ |get !(@inner [$src ] [$t ] ) ) .flatten () .collect ::<Vec <_ >>() } } ;(@inner [$src :expr ] $t :ty ) =>{{let mut buf =String ::new () ;$src .read_line (&mut buf ) .unwrap () ;buf .trim () .split_whitespace () .next () .unwrap () .parse ::<$t >() .unwrap () } } ;(@inner_elem_parse [usize1 ] $elem :expr ) =>{{get !(@inner_elem_parse [usize ] $elem ) -1 } } ;(@inner_elem_parse [$t :ty ] $elem :expr ) =>{{$elem .parse ::<$t >() .unwrap () } } ;($tt :tt ) =>{{use std ::io ::BufRead ;let get_stdin =std ::io ::stdin () ;let mut locked_stdin =get_stdin .lock () ;get !(@inner [&mut locked_stdin ] $tt ) } } ;}
macro_rules !debug {($($a :expr ) ,*$(,) *) =>{#[cfg (debug_assertions ) ] eprintln !(concat !($("| " ,stringify !($a ) ,"={:?} " ) ,*,"|" ) ,$(&$a ) ,*) ;} ;}
macro_rules !echo {($($a :expr ) ,*) =>{let mut s =Vec ::new () ;$(s .push (format !("{}" ,$a ) ) ;) *println !("{}" ,s .join (" " ) ) ;} }
#[macro_export]
macro_rules !chmin {($base :ident ,$($cmps :expr ) ,+$(,) *) =>{$base =min !($base ,$($cmps ) ,+) ;} ;}
#[macro_export]
macro_rules !chmax {($base :ident ,$($cmps :expr ) ,+$(,) *) =>{$base =max !($base ,$($cmps ) ,+) ;} ;}
#[macro_export]
macro_rules !min {($a :expr ,$b :expr $(,) *) =>{{std ::cmp ::min ($a ,$b ) } } ;($a :expr ,$($rest :expr ) ,+$(,) *) =>{{std ::cmp ::min ($a ,min !($($rest ) ,+) ) } } ;}
#[macro_export]
macro_rules !max {($a :expr ,$b :expr $(,) *) =>{{std ::cmp ::max ($a ,$b ) } } ;($a :expr ,$($rest :expr ) ,+$(,) *) =>{{std ::cmp ::max ($a ,max !($($rest ) ,+) ) } } ;}
const BIG_STACK_SIZE: bool = true;
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
fn solve() {
    let (N, K) = get!((usize, i64));
    let mut A = get!([i64]);
    A.sort();
    let max_a = A[N - 1];
    let init = A[0];
    let gcd_all = A.into_iter().fold(init, |acc, cur| gcd(acc, cur));
    if K <= max_a && K % gcd_all == 0 {
        echo!("POSSIBLE");
    } else {
        echo!("IMPOSSIBLE");
    }
}

fn gcd(a: i64, b: i64) -> i64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}