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 check(d1, k1, d2, k2):
    n1 = n*k1 // d1
    m1 = m*k2 // d2
    if n1 * m1 == 2 * n * m // k and n1 <= n and m1 <= m:   
        print("YES")
        print(0, 0)
        print(n1, 0)
        print(0, m1)
        exit()    
read = lambda: map(int, input().split())
gcd = lambda a, b: a if b == 0 else gcd(b, a % b)
n, m, k = read()
if (2 * n * m) % k:
    print("NO")
    exit()
d = 1
while d * d <= k:
    if k % d == 0:
        d2 = k // d
        d1 = d
        check(d1, 1, d2, 2)
        check(d2, 1, d1, 2)
        check(d1, 2, d2, 1)
        check(d2, 2, d1, 1)        
    d += 1
print("NO")