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.
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1000002;
const int MOD2 = 998244353;
const int MOD = 1000000007;
const int INF = 1e8;
const long double EPS = 1e-7;
long long int mul(long long int x, long long int y) {
  return (x * 1ll * y) % MOD;
}
long long int fastpow(long long int x, long long int y) {
  long long int z = 1;
  while (y) {
    if (y & 1) z = mul(z, x);
    x = mul(x, x);
    y >>= 1;
  }
  return z;
}
long long int modinv(long long int n, long long int p) {
  return fastpow(n, p - 2);
}
struct Comp {
  bool operator()(const std::pair<int, int>& a, const std::pair<int, int>& b) {
    if (a.first != b.first) {
      return a.first < b.first;
    }
    return a.second > b.second;
  }
};
int main(int argc, char** argv) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  {
    long long int n, m, k;
    cin >> n >> m >> k;
    if ((2 * n * m) % k == 0) {
      long long int u = k;
      cout << "YES\n";
      multiset<long long int> m2;
      long long int flag = 0;
      if (k % 2 == 0) {
        u /= 2;
        flag = 1;
      }
      for (int i = 2; i <= sqrt(k); i++) {
        while (u % i == 0) {
          m2.insert(i);
          u /= i;
        }
      }
      if (u > 1) m2.insert(u);
      long long int x = n, y = m;
      multiset<long long int> m1;
      for (auto f : m2) {
        if (n % f == 0) {
          n /= f;
          m1.insert(f);
        }
      }
      for (auto f : m1) {
        auto it = m2.find(f);
        m2.erase(it);
      }
      for (auto f : m2) m /= f;
      if (flag == 0) {
        if (n * 2 <= x)
          n *= 2;
        else
          m *= 2;
      }
      cout << 0 << " " << 0 << "\n";
      cout << n << " " << 0 << "\n";
      cout << 0 << " " << m << "\n";
    } else
      cout << "NO\n";
  }
  return 0;
}
