"Amazing" integers k

An integer k k is called "amazing" if the sum of the last digits of 1 k , 2 k , 3 k , 4 k , 5 k , 6 k , 7 k , 8 k 1^{k}, 2^{k}, 3^{k}, 4^{k}, 5^{k}, 6^{k}, 7^{k}, 8^{k} and 9 k 9^{k} is equal to 45. How many "amazing" integers are there between 0 and 2018?


The answer is 1009.

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