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.
import sys
import math
n,m,k=map(int,sys.stdin.readline().split())
bh=n*m*2/k
#print(int(bh),'bh')
if bh%1!=0:
    print('NO')
    sys.exit()
if k%2==0:
    g=math.gcd(k//2,n)
    a=n//g
    if m%(k//(2*g))!=0:
        print('NO')
        sys.exit()
    b=m//(k//(2*g))
else:
    g=math.gcd(k,n)
    #print(g,'g')
    a=n//g
    z=k//g
    if m%z!=0:
        print('NO')
        sys.exit()
    b=m//(k//g)
    if 2*a<=n:
        a=2*a
        #b=m//(k//g)
    else:
        b=2*b

print('YES')
print(0,0)
print(a,0)
print(0,b)
