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): 
    if(b==0): 
        return a 
    else: 
        return gcd(b,a%b) 

n,m,k=map(int,raw_input().split())
if 2*m*n%k!=0:print("NO")
else:
    print "YES"
    print 0,0
    if k%2==0:
        k1=(2*m*n)/k
        A=gcd(k1,max(m,n))
        B=k1/A
        if n>m:
            print A,0
            print 0,B
        else:
            print 0,A
            print B,0
    else:
        if m%k==0:
            A=2*m/k
            B=n
            print 0,A
            print B,0
        elif n%k==0:
            B=2*n/k
            A=m
            print 0,A
            print B,0
        else:
            k1=(2*m*n)/k
            A=gcd(k1,max(m,n))
            B=k1/A
            if n>m:
                print A,0
                print 0,B
            else:
                print 0,A
                print B,0



