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())
if (n * m * 2 % k != 0):
    print("NO")
else:
    print("YES")
    tn = n
    tm = m
    ned = True
    if (k % 2 == 0):
        k //= 2
        ned = False
    i = 2
    while (i ** 2 <= k):
        while (k % i == 0 and (tm % i == 0 or tn % i == 0)):
            if (tm % i == 0):
                if (ned):
                    tm *= 2
                    ned = False
                tm //= i
            elif (tn % i == 0):
                if (ned):
                    tn *= 2
                    ned = False                
                tn //= i
            k //= i
        i += 1
    if (k != 1):
        if (tm % k == 0):
            if (ned):
                tm *= 2
                ned = False            
            tm //= k
        else:
            if (ned):
                tn *= 2
                ned = False            
            tn //= k
    print(0, 0)
    print(0, tm)
    print(tn, 0)