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.
import math, sys
from itertools import permutations

def mp():
    return list(map(int, input().split()))

debug = 0
if debug:
    file = open("input.txt", "r")
    input = file.readline
else:
    input = sys.stdin.readline

def main():
    n, m, k = mp()
    x = n * m
    g = math.gcd(x, k)
    x //= g
    a = 0
    if k // g == 1:
        a = x * 2
    elif k // g == 2:
        a = x
    else:
        print("NO")
        return
    print("YES")
    kn = math.gcd(k, n)
    k //= kn
    km = math.gcd(k, m)
    on = n
    om = m
    n //= kn
    m //= km
    t = a // (n * m)
    if t * n <= on:
        print(0, 0)
        print(t * n, 0)
        print(0, m)
    elif t * m <= om:
        print(0, 0)
        print(n, 0)
        print(0, m * t)
    else:
        # assert(t == 4)
        print(0, 0)
        print(2 * n, 0)
        print(0, 2 * m)



main()