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.
def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a
    

n, m, k = map(int, input().split())
if n * m * 2 % k != 0:
    print('NO')
else:
    #print('YES')
    s2 = n * m * 2 // k
    ans = [(0, 0)]
    
    """i = 1
    while i * i <= s2:
        if s2 % i == 0:
            if i <= n and s2 // i <= m:
                ans.append((i, 0))
                ans.append((0, s2 // i))
                break
            if s2 // i <= n and i <= m:
                ans.append((s2 // i, 0))
                ans.append((0, i))
                break
        i += 1
    if ans == [(0, 0)]:
        print('NO')
    else:
        print('YES')
        for i in ans:
            print(i[0], i[1])"""
    
    xx1 = n // gcd(n, k)
    yy1 = s2 // xx1
    
    
    yy2 = m // gcd(m, k)
    xx2 = s2 // yy2
    
    if s2 % n == 0:
        print('YES')
        print(0, 0)
        print(n, 0)
        print(0, s2 // n)
    elif s2 % m == 0:
        print('YES')
        print(0, 0)
        print(s2 // m, 0)
        print(0, m)
    elif xx1 <= n and yy1 <= m and xx1 * yy1 == n * m * 2 // k:
        print('YES')
        print(0, 0)
        print(xx1, 0)
        print(0, yy1)
    elif xx2 <= n and yy2 <= m and xx2 * yy2 == n * m * 2 // k:
        print('YES')
        print(0, 0)
        print(xx2, 0)
        print(0, yy2)        
    else:
        print('NO')
    