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.
from fractions import gcd

ans = False
x1=0
y1=0
y2=0
x3=0
n, m, k = input().split(" ")
n = int(n)
m = int(m)
k = int(k)
a=gcd(n, k)
n_new=n/a
k_new=k/a
a = gcd(m, k_new)
m_new=m/a
k_new=k_new/a
if k_new > 2:
    print("NO")
else:
    x2 = int(n_new)
    y3 = int(m_new)
    if(k_new < 2):
        if(x2*2 <= n):
            x2*=2
            ans = True
        elif(y3*2 <= m):
            y3*=2
            ans = True
        else:
            print("NO")
    else:
        ans = True
    if(ans):
        print("YES")
        print(x1, y1)
        print(x2, y2)
        print(x3, y3)
    
