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 b == 0:
       return a
    else:
       return gcd(b, a % b)




n,m,k = map(int,raw_input().split())

was_even = False

if (2*n*m)%k == 0:

    if k%2 == 0:
        k =k/2
        was_even = True

    g = gcd(k,n)
    k_j = k/g
    a = n/g
    b = m/k_j

    if was_even == False:
        if a*2<n:
            a = a*2
        else:
            b = b*2

    print 'YES'
    print 0,0
    print a,0
    print 0,b

else:
    print 'NO'



