A fast, iterative techique for evaluating M modulo J which may be easily implemented in hardware. The methods include receiving payment instructions for a plurality of predetermined locations associated with a plurality of merchants, determining a location of a user, automatically transmitting a payment request when the user is within a predetermined distance of one of the predetermined locations, receiving a payment confirmation from the user, and processing the payment request. To this end, it is determined if the dual mode mobile terminal is in a shadow area by counting the number of ping-pong occurrences in the process of performing a mode based on a corresponding communication service and a ping-pong period is adjusted only when the dual mode mobile terminal is in the shadow area, thereby minimizing a ping-pong phenomenon. The relay is moved into a latched open position when a first winding of a coil of the relay is energized by electricity, and is moved back into a latched closed position when a second winding of the coil is energized. Each petal or supplemental key may in turn present one or more sub petals or modifier keys emanating from the supplemental key. The magnetic fixing unit further includes a guide structure on one of the first and second assemblies to effect cooperative locking engagement with an engaging member on the other of the assemblies.