Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
G. To Make 1

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputThere are $$$n$$$ positive integers written on the blackboard. Also, a positive number $$$k \geq 2$$$ is chosen, and none of the numbers on the blackboard are divisible by $$$k$$$. In one operation, you can choose any two integers $$$x$$$ and $$$y$$$, erase them and write one extra number $$$f(x + y)$$$, where $$$f(x)$$$ is equal to $$$x$$$ if $$$x$$$ is not divisible by $$$k$$$, otherwise $$$f(x) = f(x / k)$$$.

In the end, there will be a single number of the blackboard. Is it possible to make the final number equal to $$$1$$$? If so, restore any sequence of operations to do so.

Input

The first line contains two integers $$$n$$$ and $$$k$$$ — the initial number of integers on the blackboard, and the chosen number ($$$2 \leq n \leq 16$$$, $$$2 \leq k \leq 2000$$$).

The second line contains $$$n$$$ positive integers $$$a_1, \ldots, a_n$$$ initially written on the blackboard. It is guaranteed that none of the numbers $$$a_i$$$ is divisible by $$$k$$$, and the sum of all $$$a_i$$$ does not exceed $$$2000$$$.

Output

If it is impossible to obtain $$$1$$$ as the final number, print "NO" in the only line.

Otherwise, print "YES" on the first line, followed by $$$n - 1$$$ lines describing operations. The $$$i$$$-th of these lines has to contain two integers $$$x_i$$$ and $$$y_i$$$ to be erased and replaced with $$$f(x_i + y_i)$$$ on the $$$i$$$-th operation. If there are several suitable ways, output any of them.

Examples

Input

2 2 1 1

Output

YES 1 1

Input

4 3 7 8 13 23

Output

YES 23 13 8 7 5 4

Input

3 4 1 2 3

Output

NO

Note

In the second sample case:

- $$$f(8 + 7) = f(15) = f(5) = 5$$$;
- $$$f(23 + 13) = f(36) = f(12) = f(4) = 4$$$;
- $$$f(5 + 4) = f(9) = f(3) = f(1) = 1$$$.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/16/2022 12:53:49 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|