Road Construction

Time limit2sMemory limit1024 MB

Summary

Two players alternately build rectangles of area at most s on an n by m grid, and the task asks whether the first player wins.

Level: Medium6 of 10
Topics: Math, Game theory
Solved: No attempts yet

Problem

Sam is not the only person who builds roads. Today he met another builder who does the same job. The two quickly found common ground and decided to play a game.

They are building a rectangular section of road of size $n \times m$ meters. Treat it as a grid of $n \times m$ cells. Before the game starts, no cell is built.

The players take turns. On a turn, a player picks any rectangle on the grid with area at most $s$ in which no cell is built yet, and builds every cell inside it. The player who cannot move loses. Sam moves first.

Determine whether Sam wins when both players play optimally.

Input

The first line contains three integers $n$ , $m$ , and $s$ ( $1 \le n, m \le 1000$ , $1 \le s \le n \times m$ ), the grid size and the maximum area of a rectangle built in one turn.

Output

If Sam can win, print YES on a single line. Otherwise, print NO.

Examples1

Example 1
Input
```
1 4 2
```
Expected output
```
YES
```