Segments - Schedule of Company's Segment Results (Detail) - USD ($) $ in Thousands	3 Months Ended								6 Months Ended	9 Months Ended	12 Months Ended
	Dec. 31, 2023	Sep. 30, 2023	Jun. 30, 2023	Mar. 31, 2023	Dec. 31, 2022	Sep. 30, 2022	Jun. 30, 2022	Mar. 31, 2022	Jun. 30, 2023	Sep. 30, 2023	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Segment Reporting Information [Line Items]
Revenues, net		$ 970,892	$ 948,174	$ 901,333					$ 1,849,507	$ 2,820,399	$ 3,757,719	$ 3,427,129	$ 2,833,736
Operating income		444,977	412,650	375,195					787,845	1,232,822	1,656,873	1,446,641	1,242,556
Depreciation and amortization		84,750	83,676	84,232					$ 167,908	$ 252,658	336,604	322,282	284,197
Operating Segments
Segment Reporting Information [Line Items]
Revenues, net	$ 937,320	970,892	948,174	901,333	$ 883,610	$ 893,000	$ 861,278	$ 789,241			3,757,719	3,427,129	2,833,736
Operating income	424,051	444,977	412,650	375,195	369,270	389,170	370,480	317,721			1,656,873	1,446,641	1,242,556
Depreciation and amortization	83,946	84,750	83,676	84,232	89,793	77,213	78,474	76,802			336,604	322,282	284,197
Capital expenditures											153,822	151,428	111,530
Long-lived assets (excluding goodwill and investments)	343,154				294,692						343,154	294,692	236,294
Vehicle Payments | Operating Segments
Segment Reporting Information [Line Items]
Revenues, net	499,758	500,632	509,630	495,490	501,082	504,388	489,827	454,741			2,005,510	1,950,038	1,689,970
Operating income	242,505	244,908	232,506	223,480	226,337	231,914	224,174	202,068			943,399	884,493	811,822
Depreciation and amortization	49,724	49,905	51,926	50,350	51,598	49,134	49,615	48,148			201,905	198,495	195,964
Capital expenditures											108,592	111,661	88,999
Long-lived assets (excluding goodwill and investments)	252,499				218,680						252,499	218,680	175,648
Corporate Payments | Operating Segments
Segment Reporting Information [Line Items]
Revenues, net	251,101	257,842	246,012	226,172	201,016	196,339	189,058	183,158			981,127	769,571	598,242
Operating income	101,092	104,903	95,708	80,382	67,159	74,999	70,092	61,312			382,085	273,562	210,290
Depreciation and amortization	20,323	20,417	17,779	20,160	24,851	15,383	16,324	16,028			78,679	72,586	52,688
Capital expenditures											25,387	20,777	11,748
Long-lived assets (excluding goodwill and investments)	48,822				39,240						48,822	39,240	33,638
Lodging Payments | Operating Segments
Segment Reporting Information [Line Items]
Revenues, net	119,929	141,389	136,564	122,334	119,074	125,961	116,900	94,576			520,216	456,511	309,619
Operating income	57,438	74,023	68,246	54,563	56,836	63,463	58,559	39,779			254,270	218,637	148,973
Depreciation and amortization	11,655	12,189	11,661	11,398	11,037	10,474	10,321	10,534			46,903	42,366	26,478
Capital expenditures											13,705	10,570	4,604
Long-lived assets (excluding goodwill and investments)	24,697				17,884						24,697	17,884	12,592
Other | Operating Segments
Segment Reporting Information [Line Items]
Revenues, net	66,532	71,029	55,968	57,337	62,438	66,312	65,493	56,766			250,866	251,009	235,905
Operating income	23,016	21,143	16,190	16,770	18,938	18,794	17,655	14,562			77,119	69,949	71,471
Depreciation and amortization	2,244	$ 2,239	$ 2,310	$ 2,324	2,307	$ 2,222	$ 2,214	$ 2,092			9,117	8,835	9,067
Capital expenditures											6,138	8,420	6,179
Long-lived assets (excluding goodwill and investments)	$ 17,136				$ 18,888						$ 17,136	$ 18,888	$ 14,416