Probability of a random variable with sequence.

Question

I want to show

$P\{[Y_n > k_n] i.o.]\} = 0 $ iff $\sum_n P[Y_1 > k_n] < \infty$

And

$P\{[Y_n > k_n] i.o.]\} = 1 $ iff $\sum_n P[Y_1 > k_n] = \infty$

Where $Y_n$, $n \ge 1$ are independent and identically distributed random variables and $k_n$ is a sequence of constants.

I tried using the Borel Zero-One Law, but I'm confused where the iff statements come from.