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.
import random


def randomized_S():
    x1, y1 = random.randint(1, 10**3), random.randint(1, 10**3)
    x2, y2 = random.randint(1, 10**3), random.randint(1, 10**3)
    x3, y3 = random.randint(1, 10**3), random.randint(1, 10**3)
    a1, a2 = x2 - x1, y2 - y1
    b1, b2 = x3 - x1, y3 - y1
    S = abs(b2*a1-a2*b1)/2
    print(S)


n, m, k = map(int, input().split())
if 2*n*m % k != 0:
    print("NO")
    exit()
else:
    #always possible
    S = (2*n*m)//k
    # make (x*w - y*z) = S
    #constraint: 0<=x,z<= n && 0<= w,y<= m 1<=S<=n*m
    #p1 = (0, 0)
    #p2 = (n, 1)
    Y = (S + n - 1)//n
    X = n*Y - S
    print("YES")
    print(0, 0)
    print(n, 1)
    print(X, Y)
