My Moped Stopped Working, What's Wrong with it? (Honda Aero 55 1983')?

I have a Honda aero 55, 1983 and I was riding it one day when it just shut off out of nowhere. I've had it about a year now and never had a problem. Oil and gas is full and when I kick start it, it sounds normal just doesn't start. Also the battery isn't bad, charged it over night and tried it with no hope. Any ideas?

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