# Are you good at Summation?

**Algebra**Level 5

\[ \Bigg [ \displaystyle\sum_{k = 1}^{1000} k ( \lceil \log_{\sqrt{2}} k \rceil - \lfloor \log_{\sqrt{2}} k \rfloor ) \Bigg ] \pmod {1000} = \ ? \]

\[ \Bigg [ \displaystyle\sum_{k = 1}^{1000} k ( \lceil \log_{\sqrt{2}} k \rceil - \lfloor \log_{\sqrt{2}} k \rfloor ) \Bigg ] \pmod {1000} = \ ? \]

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