Are you good at Summation?

Algebra Level 5

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


The problem is not original , I found it nice so posted it here.
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