CF1684G.Euclid Guess

Let's consider Euclid's algorithm for finding the greatest common divisor, where $t$ is a list:

<pre class="verbatim"><br></br>function Euclid(a, b):<br></br>    if a < b:<br></br>        swap(a, b)<br></br><br></br>    if b == 0:<br></br>        return a<br></br><br></br>    r = reminder from dividing a by b<br></br>    if r > 0:<br></br>        append r to the back of t<br></br><br></br>    return Euclid(b, r)<br></br>

There is an array $p$ of pairs of positive integers that are not greater than $m$ . Initially, the list $t$ is empty. Then the function is run on each pair in $p$ . After that the list $t$ is shuffled and given to you.

You have to find an array $p$ of any size not greater than $2 \cdot 10^4$ that produces the given list $t$ , or tell that no such array exists.

The first line contains two integers $n$ and $m$ ( $1 \le n \le 10^3$ , $1 \le m \le 10^9$ ) — the length of the array $t$ and the constraint for integers in pairs.

The second line contains $n$ integers $t_1, t_2, \ldots, t_n$ ( $1 \le t_i \le m$ ) — the elements of the array $t$ .

• If the answer does not exist, output $-1$ .
• If the answer exists, in the first line output $k$ ( $1 \le k \le 2 \cdot 10^4$ ) — the size of your array $p$ , i. e. the number of pairs in the answer. The $i$ -th of the next $k$ lines should contain two integers $a_i$ and $b_i$ ( $1 \le a_i, b_i \le m$ ) — the $i$ -th pair in $p$ .

If there are multiple valid answers you can output any of them.

In the first sample let's consider the array $t$ for each pair:

• $(19,\, 11)$ : $t = [8, 3, 2, 1]$ ;
• $(15,\, 9)$ : $t = [6, 3]$ ;
• $(3,\, 7)$ : $t = [1]$ .

So in total $t = [8, 3, 2, 1, 6, 3, 1]$ , which is the same as the input $t$ (up to a permutation).

In the second test case it is impossible to find such array $p$ of pairs that all integers are not greater than $10$ and $t = [7, 1]$

In the third test case for the pair $(15,\, 8)$ array $t$ will be $[7, 1]$ .