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;
class Solution {
 public:
  vector<pair<int, int>> build(int n, int m, int k) {
    vector<pair<int, int>> res;
    long long x = 0, y = 0;
    if ((2LL * n * m) % k != 0) {
      res.clear();
      return res;
    }
    int nk = k;
    if (nk % 2 == 0) {
      nk /= 2;
    }
    res.resize(3);
    res[0] = make_pair(0, 0);
    auto g1 = gcd(n, nk);
    auto g2 = gcd(m, nk / g1);
    if (k % 2 == 0) {
      x = n / g1;
      y = m / g2;
    } else {
      if (g1 > 1) {
        x = 2LL * n / g1;
        y = (2LL * n * m) / k / x;
      } else {
        x = n;
        y = (2LL * n * m) / k / x;
      }
    }
    res[1] = make_pair(x, 0);
    res[2] = make_pair(0, y);
    return res;
  }

 private:
  long long gcd(long long a, long long b) { return a == 0 ? b : gcd(b % a, a); }
  bool check(vector<pair<int, int>>& pv, int n, int m, int k) {
    bool res = true;
    for (auto& p : pv) {
      int x = p.first, y = p.second;
      if (!(x >= 0 && x <= n && y >= 0 && y <= m)) {
        cout << "ERROR: out of range - " << x << "," << y << endl;
        res = false;
      }
    }
    if (area(pv) * k != 2LL * n * m) {
      cout << "Incorrect area: " << area(pv) << endl;
      res = false;
    }
    return res;
  }
  long long area(vector<pair<int, int>>& pv) {
    int x0 = pv[0].first, y0 = pv[0].second;
    int x1 = pv[1].first, y1 = pv[1].second;
    int x2 = pv[2].first, y2 = pv[2].second;
    return abs((x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0));
  }
};
int main(int argc, char** argv) {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m, k;
  cin >> n >> m >> k;
  Solution sol;
  auto res = sol.build(n, m, k);
  if (res.empty()) {
    cout << "NO" << endl;
  } else {
    cout << "YES" << endl;
    for (auto& p : res) {
      cout << p.first << " " << p.second << endl;
    }
  }
  return 0;
}
