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 math
n, m, k = map(int, input().split())
ind= False
q= int(math.sqrt(n))
for i in range(1, q + 1):
    if (n % i == 0 or m % i == 0):
        l= int(0)
        r= m
        while (r - l > 1):
            mid= (r + l) // 2
            if mid * i * k >= 2 * m * n:
                r= mid
            else:
                l= mid
                
        if r * i * k == 2 * n * m:
            ind= True
            print("YES\n0 0\n", 0, " ", r, "\n", i, " 0", sep= "")
        else:
            j= n // i
            r= m
            l= int(0)
            while r - l > 1:
                mid= (r + l) // 2
                if mid * j * k >= 2 * m * n:
                    r= mid
                else:
                    l= mid
                    
            if r * j * k == 2 * n * m:
                ind= True
                print("YES\n0 0\n", 0, " ", r, "\n", j, " 0", sep= "")
    if ind:
        break;

q= int(math.sqrt(m))

for i in range(1, q + 1):
    if ind:
        break
    if (n % i == 0 or m % i == 0):
        l= int(0)
        r= n
        while (r - l > 1):
            mid= (r + l) // 2
            if mid * i * k >= 2 * m * n:
                r= mid
            else:
                l= mid
                
        if r * i * k == 2 * n * m:
            ind= True
            print("YES\n0 0\n", 0, " ", i, "\n", r, " 0", sep= "")
        else:
            j= m // i
            r= n
            l= int(0)
            while r - l > 1:
                mid= (r + l) // 2
                if mid * j * k >= 2 * m * n:
                    r= mid
                else:
                    l= mid
                    
            if r * j * k == 2 * n * m:
                ind= True
                print("YES\n0 0\n", 0, " ", j, "\n", r, " 0", sep= "")
    if ind:
        break;
                
if not(ind):
    print("NO")