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Borrowings - Schedule of Long-term Debt (Details) £ in Thousands, $ in Thousands	12 Months Ended
	Sep. 30, 2022 USD ($)	Sep. 30, 2022 GBP (£)	Oct. 01, 2021 USD ($)
Debt Instrument [Line Items]
Total Long-term debt, net	$ 3,357,256		$ 2,839,933
Less: Current Portion	(50,415)		(53,456)
Less: Deferred Financing Fees	(3,466)		(5,069)
Term Loan Facility 2021
Debt Instrument [Line Items]
Total Long-term debt, net	923,580		1,081,724
Term Loan Facility 2020
Debt Instrument [Line Items]
Total Long-term debt, net	$ 882,263		988,940
Quarterly principal payment, percent of aggregate borrowings	1.25%
Quarterly principal payment	$ 9,125	£ 3,125
Senior Notes, Series A
Debt Instrument [Line Items]
Total Long-term debt, net	$ 190,000		190,000
Stated interest rate	4.27%
Senior Notes, Series B
Debt Instrument [Line Items]
Total Long-term debt, net	$ 180,000		180,000
Stated interest rate	4.42%
Senior Notes, Series C
Debt Instrument [Line Items]
Total Long-term debt, net	$ 130,000		130,000
Stated interest rate	4.52%
Revolving Credit Facility
Debt Instrument [Line Items]
Total Long-term debt, net	$ 1,105,294		$ 327,794
Eurocurrency Interest Rate | Term Loan Facility 2020
Debt Instrument [Line Items]
Margin added to variable rate interest rate	3.60%	3.60%
Eurocurrency Interest Rate | Revolving Credit Facility
Debt Instrument [Line Items]
Margin added to variable rate interest rate	3.60%	3.60%
Eurocurrency Interest Rate | Minimum | Term Loan Facility 2021
Debt Instrument [Line Items]
Margin added to variable rate interest rate	0.875%	0.875%
Eurocurrency Interest Rate | Minimum | Term Loan Facility 2020
Debt Instrument [Line Items]
Margin added to variable rate interest rate	0.875%	0.875%
Eurocurrency Interest Rate | Maximum | Term Loan Facility 2021
Debt Instrument [Line Items]
Margin added to variable rate interest rate	1.625%	1.625%
Eurocurrency Interest Rate | Maximum | Term Loan Facility 2020
Debt Instrument [Line Items]
Margin added to variable rate interest rate	1.50%	1.50%
Base Interest Rate | Minimum | Term Loan Facility 2021
Debt Instrument [Line Items]
Margin added to variable rate interest rate	0.00%	0.00%
Base Interest Rate | Minimum | Term Loan Facility 2020
Debt Instrument [Line Items]
Margin added to variable rate interest rate	0.00%	0.00%
Base Interest Rate | Minimum | Revolving Credit Facility
Debt Instrument [Line Items]
Margin added to variable rate interest rate	0.00%	0.00%
Base Interest Rate | Maximum | Term Loan Facility 2021
Debt Instrument [Line Items]
Margin added to variable rate interest rate	0.625%	0.625%
Base Interest Rate | Maximum | Term Loan Facility 2020
Debt Instrument [Line Items]
Margin added to variable rate interest rate	50.00%	50.00%
Base Interest Rate | Maximum | Revolving Credit Facility
Debt Instrument [Line Items]
Margin added to variable rate interest rate	0.625%	0.625%
LIBOR | Term Loan Facility 2021
Debt Instrument [Line Items]
Margin added to variable rate interest rate	4.06%	4.06%	1.43%
LIBOR | Maximum | Term Loan Facility 2020
Debt Instrument [Line Items]
Margin added to variable rate interest rate	4.49%	4.49%	1.45%
LIBOR | Maximum | Revolving Credit Facility
Debt Instrument [Line Items]
Margin added to variable rate interest rate	4.08%	4.08%	1.45%
Sterling Overnight Interbank Average Rate | Minimum | Revolving Credit Facility
Debt Instrument [Line Items]
Margin added to variable rate interest rate	0.875%	0.875%
Sterling Overnight Interbank Average Rate | Maximum | Revolving Credit Facility
Debt Instrument [Line Items]
Margin added to variable rate interest rate	1.625%	1.625%

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