404191: GYM101446 E Construct the Polygon

Construct a convex polygon with the following properties (ot determine that the construction is impossible):

• Coordinates of all vertices of the polygon are integers.
• All coordinates satisfy the inequalities 0 ≤ x_i ≤ n, 0 ≤ y_i ≤ m.
• Number of vertices should not exceed 10⁵.
• No three vertices of the polygon lie on a common straight line.
• Area of the polygon is equal to S.

The only line of input contains two positive integers n and m (1 ≤ n, m ≤ 10⁵) — upper bounds on coordinates, and one real number S (0 < S ≤ 10⁹) — desired area of the polygon given with at most 6 digits after the decimal point.

If it is impossible to construct a suitable polygon, print  - 1.

Otherwise, on the first line print k — number of vertices in your polygon (3 ≤ k ≤ 10⁵). On each of the next k lines print x_i and y_i — coordinates of the vertices of the polygon (0 ≤ x_i ≤ n, 0 ≤ y_i ≤ m) listed in clockwise order.

10 10 81

5
0 0
0 7
9 9
10 9
10 0

1 2 0.5

3
0 0
0 1
1 1