Parking lot#713
The parking lot is arranged in a circle, with all parking spaces numbered consecutively from to . Cars arrive and leave throughout the day, each aiming for a specific parking space designated for its owner. If the desired space is occupied, the car moves clockwise (following the order 1, 2, 3, \ldots, n, 1, 2, 3, \ldots) until it finds an available spot and parks there. If no spaces are available, the car leaves without parking.
The first line contains two integers 1 \leq n,\ m \leq 100\ 000, where is the total number of parking spaces, and is the number of events during the day. Each event is either a car's arrival or departure. Each of the following lines describes one event. A car's arrival is written as "+ i" (with a space between the "+" sign and the number), where is the initial target space for the car. Departure is denoted as "- i" (with a space between the "-" sign and the number), where is the parking space number.
For each car arrival, output a single line with the number of the space where the car parked, or if no space was available. For each car departure, output if a car was indeed parked in that space, and if there was no car at space .
Example 1