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.
#I_AM_L
l=input().split()
n=int(l[0])
m=int(l[1])
k=int(l[2])
mo=2*n*m
if(mo%k!=0):
    print("NO")
else:
    lfi=[]
    i=1
    while(i*i<=k):
        if(k%i==0):
            if(i!=k//i):
                lfi.append(i)
                lfi.append(k//i)
            else:
                lfi.append(i)
        i+=1
    ans=0
    for i in  lfi:
        if((2*n)%i==0 and m%(k//i)==0 and i>=2):
            ans=i
            break
    if(ans!=0):
        print("YES")
        print(0,0)
        print((2*n)//ans,0)
        print(0,m//(k//ans))
    else:

        for i in  lfi:
            if((n)%i==0 and (2*m)%(k//i)==0 and k//i>=2):
                ans=i
                break
        print("YES")
        print(0,0)
        print(n//ans,0)
        print(0,(2*m)//(k//ans))