Before revision:  This improves over the best-known amortized update time of (n^{1/k)\cdot(1/\epsilon)^{O(\sqrt{\log n})} }  [Chechik, FOCS'18] . Moreover, we reduce the query time from O(\log \log(nW)) to a constant O(k), and hence eliminate the dependence on nand the aspect ratio W\cdot(\frac{1}{\epsilon})^{\tilde{O}(\sqrt{\log n})}.
After revision:  This improves over the best-known amortized update time of (n^{1/k)\cdot(1/\epsilon)^{O(\sqrt{\log n})} } significantly improves (by a polynomial factor) over the update-time of the best previously known decremental algorithm in the constant query time regime. Moreover, it improves over the result of [Chechik, FOCS'18] . Moreover, we reduce the query time from O(\log \log(nW)) to a constant O(k), and hence eliminate the dependence on nand the aspect ratio W\cdot(\frac{1}{\epsilon})^{\tilde{O}(\sqrt{\log n})}.