Problem Statement

You are given positive integers $N$, $M$, and $B$ as input.

$\displaystyle x_0^2 + x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 \equiv M^N \pmod{B} $

Determine whether there exists a combination $(x_0,x_1,x_2,x_3,x_4,x_5)$ of positive integers at most $10^9$ satisfying the above, and if one exists, find $1$ such $(x_0,x_1,x_2,x_3,x_4,x_5)$.

Input

The input is given from standard input in the following format:

$N$ $M$ $B$

$N, M, B$ are given on $1$ line, separated by spaces.

Constraints

The input satisfies the following constraints:

• $N$ is a positive integer at most $10^{18}$
• $M$ is a positive integer at most $10^3$
• $B$ is a positive integer at most $10^9$

Output

$\displaystyle x_0^2 + x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 \equiv M^N \pmod{B} $

If there exists no combination $(x_0,x_1,x_2,x_3,x_4,x_5)$ of positive integers at most $10^9$ satisfying the above, output NO.

If one exists, output YES on the $1$st line, and output such $x_0,x_1,x_2,x_3,x_4,x_5$ separated by spaces on the $2$nd line.

This is a special judge problem. There may be more than $1$ correct answer, but output only $1$ of them.

Print a newline at the end.

Sample

1 2 2

YES
1 1 1 1 1 1

2 3 4

YES
2 1 1 1 1 1

3 4 11

YES
2 1 2 1 1 3