Minimum value?

Algebra Level 4

If \(\log_4 (x+2y)+ \log_4 (x-2y) = 1\), and the minimum value of \(|x|-|y|\) is \(k\), then find \(\lceil k \rceil\).

Notation: \( \lceil \cdot \rceil \) denotes the ceiling function.


Source: This is a problem from the China Mathematics Competition (2002).
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