Problem applying to two programs !!

Hello Ladies and Gentlemen

I have a small trouble here
I would like to apply to two international programs (for my PhD) in two separate universities (KYOTO and TOKYO)
I like both programs and I have contacted profs in both and they told me I should apply first ...I am afraid if I got accepted and nominated to MEXT...I will be disqualified for being nominated from two univs

But I afraid to apply for one and then get rejected ...so do you know what to do? would any program tell me before nominate me to mext ? can I cancel my nomination from one program if I like ?

Any help is highly appreciated

before you are nominated, your professor and the school will check to make sure that you will accept. At that time you will need to make a choice.