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
n, m, k = [int(x) for x in input().split()]

if 2*n*m % k != 0:
    print('NO')
else:
    if k % 2 == 0:
        k //= 2
        g = math.gcd(k, n)
        k1 = k // g
        a = n // g
        b = m // k1
    else:
        g = math.gcd(k, n)
        a = n // g
        k1 = k // g
        b = m // k1
        if a < n:  # if a = n then b always < m
            a *= 2
        else:
            b *= 2
    print('YES')
    print(0, 0)
    print(a, 0)
    print(0, b)