Show that the following modifications of the Post correspondence problem are undecidable.
$\text(a)$ There is an MPC solution if there is a sequence of integers such that $w_iw_j...w_kw_1 = v_iv_j...v_kv_i$.
$\text(b)$ There is an MPC solution if there is a sequence of integers such that $w_1w_2w_iw_j...w_k = v_1v_2v_iv_j...v_k$.
