Simulate left-censored time-to-event data

Hello, I simulated random variables from a Weibull distribution using the following code:

r=rand(1000, 1);
t=wblinv(r, 1,0.5);

The vector t here includes the end dates of an event for 1000 observations. Suppose that for some of the variables in the t vector, the end date of the event is equal to the total duration of the event. But for other observations, the total duration is longer than t because their durations are left-censored, i.e., their total duration tt is equal to t+ta. How can I simulate such left-censored data?