Garden Flower Arrangement

You are given three positive integers n, m and f. They represent an n \times m grid of flower beds and a total of f flowers. You want to plant exactly f flowers in the grid such that:

• Each flower bed receives at least one flower, and
• The difference between the number of flowers in any two beds is at most \(1\).

The arrangement is possible if and only if \(f \ge n\times m\) and the number of extra flowers \(f - n\times m\) satisfies \[ (f - n\times m) \bmod (n\times m) \le 1. \] Determine whether it is possible to achieve such an arrangement. Print YES if it is possible; otherwise, print NO.

inputFormat

The input is read from stdin and consists of a single line containing three space-separated integers: n, m, and f.

outputFormat

Print a single line to stdout with either YES if the arrangement is possible or NO if it is not.

3 3 9

YES