Vasya has got three integers n, m and k. He'd like to find three integer points (x_1, y_1), (x_2, y_2), (x_3, y_3), such that 0 ≤ x_1, x_2, x_3 ≤ n, 0 ≤ y_1, y_2, y_3 ≤ m and the area of the triangle formed by these points is equal to nm/k.

Help Vasya! Find such points (if it's possible). If there are multiple solutions, print any of them.

Input

The single line contains three integers n, m, k (1≤ n, m ≤ 10^9, 2 ≤ k ≤ 10^9).

Output

If there are no such points, print "NO".

Otherwise print "YES" in the first line. The next three lines should contain integers x_i, y_i — coordinates of the points, one point per line. If there are multiple solutions, print any of them.

You can print each letter in any case (upper or lower).

Examples

Input

4 3 3


Output

YES
1 0
2 3
4 1


Input

4 4 7


Output

NO

Note

In the first example area of the triangle should be equal to nm/k = 4. The triangle mentioned in the output is pictured below: 

<image>

In the second example there is no triangle with area nm/k = 16/7.
# -*- coding: utf-8 -*-
"""
Created on Sun Sep 23 08:57:05 2018

@author: yanni
"""

import math

def small_factor(N, d=1):
    if N == 1:
        return 1
    if d == 1:
        d = 2
    for D in range(d, int(math.sqrt(N) + 2)):
        if (N % D == 0):
            return D
    return N

n, m, k = [int(x) for x in input().split()]
P = 2*n*m
two = True
if (P%k != 0):
    print("NO")
else:
    if (k % 2 == 0):
        k = k // 2
        two = False
    K = k
    d = 1
    N = n
    M = m
    good = True
    while (K > 1):
        d = small_factor(K, d)
        K = K // d
        if (N % d == 0):
            N //= d
        elif (M % d == 0):
            M //= d
        else:
            print("NO")
            good = False
            break
    if (two):
        if (N <= n//2):
            N *= 2
        else:
            M *= 2
    if (good):
        print("YES")
        print("0 0")
        print(N, "0")
        print("0", M)
    