2017 AMC10B P14  An integer $$N$$ is selected at random in the range $$1\leqslant N\leqslant2020$$. What is the probability that the remainder when $$N^{16}$$ is divided by $$5$$ is $$1$$?  在$1\leqslant N\leqslant2020$的范围内随机选择一个整数$N$。当$N^{16}$除以$5$时，余数是$1$的概率是多少？
选项为:A:$$\frac 15$$  B:$$\frac 25$$  C:$$\frac 35$$  D:$$\frac 45$$  E:$$1$$  请回答其中一个选项.