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.
USE_STDIO = False

if not USE_STDIO:
    try: import mypc
    except: pass

def main():
    n, m, k = map(int, input().split(' '))
    if 2 * m * n % k:
        print('NO')
        return
    print('YES')
    t = 2 * m * n // k
    if k == 2:
        x1, y1 = 0, 0
        x2, y2 = 0, m
        x3, y3 = n, 0
    elif t <= m:
        x1, y1 = 0, 0
        x2, y2 = 1, 0
        x3, y3 = 0, t
    else:
        q = t // m
        p = m * (q + 1) - t
        x1, y1 = 0, 0
        x2, y2 = 1, m
        x3, y3 = q + 1, p
    print(x1, y1)
    print(x2, y2)
    print(x3, y3)


if __name__ == '__main__':
    main()



