Body of question
Note: this is THEORETICAL exercise. I understand OTP and CBC does not get along.
I have to find a CPA on CBC enc-mode using OTP as the encryption algorithm, s.t a new key is generated only for every new message, but not for every block.
Second question is whether this method is not safe at all, or, it could be safe for odd block number, or perhaps for even block number?
What I've tried myself
I can see myself that in even block number case, the key is cancelled out at last (thanks to CBC), so what I get is $IV \oplus P_1 \oplus...\oplus P_n$, but can't think of a way to distinguish two messages with the IND-test for CPA.
Basically I can calculate the blocks of each $m_1,m_2$ that I use for the test, but the randomized IV will prevent me from knowing what message is the ciphered text retrieved from the test...
And what about the odd case?