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 (b == 0):
        return a
    return gcd(b, a % b)


n, m, k = map(int, input().split())
if ((2 * n * m) % k != 0):
    print("NO")
else:
    s = (2 * n * m) // k
    x = gcd(n, s)
    y = s // (gcd(n, s))
    if (y <= m):
        print("YES")
        print(0, 0)
        print(x, 0)
        print(0, y)
    else:
        y = gcd(m, s)
        x = s // (gcd(m, s))
        if (x <= n):
            print("YES")
            print(0, 0)
            print(x, 0)
            print(0, y)
        else:
            print("NO")