The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Unknown Language Round 3 |
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Finished |

The following languages are only available languages for the problems from the contest

Unknown Language Round 3:

- Pike 7.8

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A. Carpeting the Room

time limit per test

2 secondsmemory limit per test

64 megabytesinput

stdinoutput

stdoutSoroush's room is a square with side length *n*. Before this contest he bought *k* fine Persian carpets to carpet his room for celebrating the 100th contest on his favorite site. Each Persian carpet is a square of side length *n*_{1}.

Soroush wants to cover all the area of his room. Carpets can be put over each other but it is not allowed to rotate the carpets. Can Soroush carpet his room completely?

Input

The input consists of three integer numbers *n*, *k* and *n*_{1} (10 ≤ *n* ≤ 12, 1 ≤ *k* ≤ 10, ).

Output

Write a single YES or NO. Write YES if and only if Sorush can carpet his room completely.

Examples

Input

10 4 6

Output

YES

Input

10 2 5

Output

NO

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