Expanding Seems Implausible

Algebra Level 5

Let ωn=eiπ/n\omega_n=e^{i\pi/n}. The value of j=12014(i=1j(ωj2i11))\left|\prod_{j=1}^{2014}\left(\prod_{i=1}^j\left(\omega_j^{2i-1}-1\right)\right)\right| can be expressed as aba^b where a,ba,b are positive integers and aa is as small as possible. What is a+ba+b?

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