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
import time
from collections import defaultdict,deque,Counter
from sys import stdin,stdout
from bisect import bisect_left,bisect_right
from queue import PriorityQueue 
import sys
def gcd(a,b):
    if(b==0):
        return a 
    return gcd(b,a%b)
n,m,k=map(int,stdin.readline().split())
N=n 
M=m
g=gcd(n,k)
n=n//g
k=k//g
g=gcd(m,k)
m=m//g
k=k//g 
if(k>2):
    print("NO")
elif(n*m)/k  >N*m:
    print("NO")
elif(k==2):
    print("YES")
    print(0,0)
    print(n,0)
    print(0,m)
else:
    if(n+n<=N):
        n+=n
    else:
        m+=m 
    print("YES")
    print(0,0)
    print(n,0)
    print(0,m)


