Question CPU cooler for an i7 9700k in a corsair air 240 case

[Tehflamex]

Im wondering which CPU cooler would be the best choice for cooling an i7 9700k in my air 240, planning to go to oc to 5 ghz.
build: https://pcpartpicker.com/list/JRmHCb

in addition, i currently have an Master liquid ML120r rgb, cpu AIO cooler, but i dont suppose that'd be nearly enough to cool that CPU , i'd also prefer to use an air cooler if possible, but the 120mm high restriction with the air 240 is rather unfortunate.

 

[NightHawkRMX]

A 120mm AIO with an overclocked 9700k isn't going to cut it, so yes, you will want a new cooler.
The H100I from Corsair is a good option and PCpartPicker says it will fit. https://pcpartpicker.com/list/DX6Fvn
What is your budget?

 

[Tehflamex]

A 120mm AIO with an overclocked 9700k isn't going to cut it, so yes, you will want a new cooler.
The H100I from Corsair is a good option and PCpartPicker says it will fit. https://pcpartpicker.com/list/DX6Fvn
What is your budget?

130$ give or take some, would it be possible to run it on the 120mm AIO without OC? ( would be cool if i could buy a better cooler later then OC ), do you have any air coolers in mind?