Determine, with proof, whether each of the following languages over = {0, 1} is regular. Here, O(t) denotes the total number of 1s in a string t.

(a) L = {s | s = 1k t, k 1, t , and O(t) k}

(b) L = {s | s = 1k t, k 1, t , and O(t) k}