Before revision:  Previously such a separation was known only for k = 2. We stress that for k= 2 , there are only finitely many distinct problems to consider. Our positive results show wider applicability of bias-based algorithms used previously by Guruswami-Velingker-Velusamy APPROX'17 , Chou-Golovnev-Velusamy FOCS'20 by giving a systematic way to explore biases.
After revision:  Previously such a separation was known only for k = 2. We stress that for k= 2 Guruswami-Velingker-Velusamy APPROX'17 , Chou-Golovnev-Velusamy FOCS'20 by giving a systematic way to explore biases.