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.

"""
0 0
a b
c d

area = 0b+ad+c0-a0-cb-0d = ad-bc

"""

import sys
#sys.stdin=open("data.txt")
input=sys.stdin.readline
mii=lambda:map(int,input().split())

n,m,k=mii()

if (2*m*n)%k!=0:
    print("NO")
else:
    print("YES")
    print("0 0")
    det=(2*m*n)//k
    a=n
    d=(det+n-1)//n
    remain=a*d-det
    b=1
    c=remain
    print("%d %d"%(a,b))
    print("%d %d"%(c,d))

