PHP confusion over reversing a DatePeriod iterator - php

Question

I'm trying to work out how to invert my date period without pushing the data into an array and reversing it.
Say I would like a list of the last 5 Saturdays the following code will produce:
$begin = new DateTime( date('Y-m-d', strtotime("last Saturday")));
$begin->modify("- 4 weeks");
$end = new DateTime( date('Y-m-d', strtotime("last Saturday")));
$end = $end->modify( '+1 day' );
$interval = new DateInterval('P1W');
$periods = new DatePeriod($begin, $interval ,$end);
foreach($periods as $date){
echo $date->format("Y-m-d") . "\n";
}
2021-07-31
2021-08-07
2021-08-14
2021-08-21
2021-08-28
I would like this list reversed. So I figured I could make use of the DatePeriod invert property. Both the start and end of the DatePeriod look correct, with a result showing in the current element. However, interating over $period returns nothing:
$begin = new DateTime( date('Y-m-d', strtotime("last Saturday")));
$begin = $begin->modify( '+1 day' );
$end = new DateTime( date('Y-m-d', strtotime("last Saturday")));
$end->modify("- 4 weeks");
$interval = new DateInterval('P1W');
$interval->invert = 1;
$periods = new DatePeriod($begin, $interval ,$end);
foreach($periods as $date){
echo $date->format("Y-m-d") . "\n";
}
Update
So I've found a solution that calculates a diff of days and passes that to the end param in the DatePeriod constructor. It's not ideal but is working. Note the diff->days had to be divided by the days interval to prevent additional dates pulling through.
$start = new \DateTime( date('Y-m-d', strtotime("last Saturday")));
$end = new DateTime( date('Y-m-d', strtotime("last Saturday")));
$end->modify("- 4 weeks");
$diff = $end->diff($start);
$interval = new \DateInterval('PT0S'); //0 duration
$interval->d = -7; //negative value
$period = new \DatePeriod($start, $interval, $diff->days / 7);
foreach ($period as $date) {
echo $date->format('Y-m-d') . PHP_EOL;
}