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=[int(k) for k in raw_input().split(" ")]

def bezout(a,b) :              # retourne (g,u,v) tel que g = a*u + b*v et g = pgcd(a,b)
    if b == 0 : return (a,1,0)
    q = a // b 
    r = a % b
    (g,u1,v1) = bezout(b,r)    
    return (g,v1,u1-q*v1)      # joli algo :-)


p=bezout(n,k)[0]

n2=n/p
k2=k/p
p=bezout(m,k2)[0]
m2=m/p
k2/=p

if k2>2:
    print "NO"
if k2==1:
    if n2<=n/2:
        n2*=2
        k2*=2
    else:
        m2*=2
        k2*=2
if k2==2:
    print "YES"
    print "0 0"
    print "{} 0".format(n2)
    print "0 {}".format(m2)
