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.
def gcd(a, b):
    if a == 0 or b == 0:
        return max(a, b)
    if a == 1 or b == 1:
        return 1
    else:
        a, b = min(a, b), max(a, b)
        return gcd(a, b % a)

n, m, k = map(int, raw_input().split())
if (2*n*m)%k != 0:
    print "NO"
else:
    gn = gcd(2*n, k)
    np = (2*n) // gn
    kp = k // gn

    if np > n:
        np = np / 2
        m = m * 2

    gm = gcd(m, kp)
    mp = m // gm

    print "YES"
    print "0 0"
    print "%d 0" % np
    print "0 %d" % mp
    

