Determine a exponential distribution of parameter

Question

Assignment:

Let y₁, y₂, ... iid rvs with exponential distribution of parameter λ. Let x be a discrete rv defined as follows

x= max {k: ^kΣ_i=1 y_i ≤ 1}

where it is understood that x = 0 if y₁ > 1. Prove that x has a Poisson distribution of parameter λ. Note that this method can be used for the computer-aided generation of instances of a Poisson distributed rv.