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.
def gcd(a,b):
    if(a==0):
        return b
    return gcd(b%a,a)

n,m,k = map(int,input().split())
flag = 1
if(k%2==0):
    flag = k%2
    k=k//2
if(n*m)%k!=0:
    print("NO")
else:
    s = gcd(n,k)
    a=n//s
    k=k//s
    b=m//k
    if(flag == 1):
        if(a<n):
            a+=a
        else:
            b+=b
    print("YES")
    print("0 0")
    print(a,"0")
    print("0",b)
# PRIYANHSU KUMAR
# Miles to go before i sleep :->>
    