Hi everyone! お久しぶりです！( = Ohisashiburi desu.) It has been a long time!
And ただいま！( = Tadaima!) I am back!!
= Ie douzo osakini!
= Oh, no, please (you) go ahead.
Or if you want to go ahead, you say,
= Soredewa osaki ni shitsurei shimasu.
= OK, then, let me go first. (←the literal meaning is…I will take the liberty of going ahead of you. or doing something before you do).
Or simply say,
= Arigatou (gozaimasu.)
= Thank you (very much)
= Sorede wa shiturei shimasu.
= If you insist.. allow me to go ahead.
Also when you leave your office or some place before other people do, it is polite to say,
= Osaki ni shitsurei shimasu.
= “Please excuse me for leaving before you.
(I am sorry to leave the office while you are still working or doing something.)”
Note : If someone leave the office before you do saying this, you say
= Otsukare sama deshita.
= (The literal meaning) You must be tired after all the hard work today.
= Thank you for your hard work. / Thank you for all your work today.
If you want to make it sound more polite, say
= Osaki ni shiturei itashimasu.
And if you are talking to your friends or in casual situation, you just say
= Osakini! / Osaki!
= Bye! I’m off! (I’ll just go ahead and leave ahead of you.)
Now お先に ( = osakini) is a formal form of 先に ( = sakini)
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I appreciate your support! サポートありがとう！