Let .

This is equivalent to the number of trailing zeros when is written in binary.

- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,

Choose so that and . Choose so that and .

Then and , so .

Let .

This is equivalent to the number of trailing zeros when is written in binary.

- ,
- ,
- ,
- ,
- ,
- ,
- ,
- ,

Choose so that and . Choose so that and .

Then and , so .

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