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 math
n,m,k=map(int,input().split())
ox=n
oy=m
kox=k
if((2*(n*m))%k!=0):
    print('NO')
else:
    n=2*n
    r=math.gcd(n,k)
    n=n//r
    k=k//r
    x=math.gcd(m,k)
    m=m//x
    k=k//x
    if(k==1):
        
        if(n<=ox and m<=oy):
            print('YES')
            print(0,0)
            print(n,0)
            print(0,m)
            exit()
        
        
    n=ox
    m=oy
    k=kox
    m=2*m
    r=math.gcd(n,k)
    n=n//r
    k=k//r
    x=math.gcd(m,k)
    m=m//x
    k=k//x
    if(k==1):
        if(m<=oy and n<=ox):
            print('YES')
            print(0,0)
            print(n,0)
            print(0,m)
            exit()
    print('NO')
        
    
    

        
       
    

