How to type in Cyrillic at my Apple US International keyboard?

It's easy to type in Cyrillic at my iPhone and my iPad, but not easy in my Mac. I own an Apple US international keyboard.

I don't want to switch or change US international to Russian Cyrillic, because I will be very confused. For example:

Q (US international) = Й (Russian Cyrillic), but Й means Y. And Y (US international) = н, which means N.

I will be confused with these keyboards.

I prefer to write in Cyrillic at US International keyboard. Is it possible?

Added (1). Vasiusal, I'm still confused with the keyboards when you explained.

Russian keyboard made for easy type. It was do for typewriter. More used keys is in center of board. There are transliteration sites in Internet for transfer russian in latin to russian in cyrillic (for example, http://translit.ru/), but i not sure that it like to you.
We (russian people) are remember both cyrillic and latin keyboard layout and it isn't problem, but is it really problem for you? I doubt.

Your approach is flawed. Russian letters do not correspond to English Latin letters 1:1. Ok, you matched y to й. What will you match to Ы? Or Q? Or Ъ? Etc, etc, etc.
ЙЦУКЕН keys are arranged under the same principle the QWERTY are arranged. You don't complain they aren't ordered according to the alphabet, right?

You should buy keyboard stickers:
http://www.ebay.com/...&_from=R40

And your complaints about non-coincidence of English and Russian letters are not serious for others, because you need not to type a lot in Russian. Positions of keys on Russian keyboard allow to type faster (the same reason why English keyboard starts from qwerty, not from abcdef… ).