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())
n1,m1,k1=n,m,k
if (n*m*2)%k==0:
    S=(n*m*2)//k
    x=0
    a, b = n, k
    while a != 0 and b != 0:
        if a > b:
            a %= b
        else:
            b %= a
    gcd = a + b
    n=n//gcd
    k=k//gcd
    a, b = m, k
    while a != 0 and b != 0:
        if a > b:
            a %= b
        else:
            b %= a
    gcd = a + b
    m=m//gcd
    k=k//gcd
    if k==1:
        if m*2<=m1:
            m*=2
        else:
            n*=2
    print('YES')
    print('0 0')
    print('0 '+str(m))
    print(str(n)+' 0')
else:
    print('NO')
