When exposed to intense light of ~580 nm, the ground state of K shifts up in energy, passing through two-photon resonances with Rydberg states and finally crossing the two-photon ionization limit. Using laser pulses of 0.5 to 13 ps duration, we have shown experimentally that ionization occurs for short pulses, but for long pulses the population is diverted into the Rydberg states where some population survives the peak intensity of the pulse, in excellent agreement with a dynamic Floquet model.