the demon hunting hero

Everything was well in ua but after izuku heard his girfriend ochako cheating on him with his ex childhood friend bakugo but what hurt him the most is tht most of his classmates knew about it but ditent tell him beacuse they ditent wanna risk him becoming a villain after hearing this he ran away but he somehow activadet a quirk that allowde him do Travel do one point in time the period where demons existed and only demon slayes hu are mostly female could hunt them but with his arrival the strongest demon slayer was born but he had do return for his quirk do recharge or other wise he would be stuck in that time and then he had do face his ex girlfriend and classmates how will izuku deal with bpth sodes will he be appeal do hmfight villains and beat demons or will he die tryng