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
    else:
        return gcd(b, a % b)
n, m, k = map(int, input().split())
if (2 * n* m % k) != 0:
    print('NO')
else:
    print('YES')
    fg = k % 2 == 0
    if fg:
        k /= 2
    g = abs(gcd(n, k))
    a = n / g
    k /= g
    b = m / k
    if fg == False:
        if a < n:
            a *= 2
        else:
            b *= 2
    print('0 0')
    print(0,int(b))
    print(int(a),0)
