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.
n,m,k=map(int,input().split())
from math import gcd
if (n*m)/k-(n*m)//k!=0 and (n*m)/k-(n*m)//k!=0.5:
    print("NO")
else:
    a=2*n
    b=2*m
    g1=gcd(a,k)
    g2=gcd(b,k)
    x=a//g1
    y=m//(k//g1)
    c=b//g2
    d=n//(k//g2)
    if x<=n and y<=m:
        print("YES")
        print(0,0)
        print(x,0)
        print(0,y)
    elif x<=m and y<=n:
        print("YES")
        print(0,0)
        print(y,0)
        print(0,x)
    elif c<=n and d<=m:
        print("YES")
        print(0,0)
        print(c,0)
        print(0,d)
    elif c<=m and d<=n:
        print("YES")
        print(0,0)
        print(d,0)
        print(0,c)
    else:
        print("NO")
        
        
                
                    
                        
        
    
    
