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.
#1030D
[n,m,k] = list(map(int,input().split()))
def gcd(a,b):
    x = max(a,b)
    y = min(a,b)
    r = x%y
    while r > 0:
        x = y
        y = r
        r = x%y
    return y
x = gcd(m,k)
y = gcd(n,k)
if x > y:
    s = (m//x)*n
else:
    s = m*(n//y)
if (2*s)%(k//max(x,y)) == 0:
    print('YES')
    s = s//(k//max(x,y))*2
    if x > y:
        print(0,0)
        if x < k:
            print(2*n//(k//x),0)
            print(0,(m//x))
        else:
            print(n//(k//x),0)
            print(0,(2*m//x))
    else:
        print(0,0)
        if y < k:
            print((n//y),0)
            print(0,2*m//(k//y))
        else:
            print(2*n//y,0)
            print(0,m//(k//y))
else:
    print('NO')
    