## Show $\{1^n0^m |\space n \neq 2^m\}$ not regular using pumping lemma

Showing that the language $$L$$ with $$\{1^n0^m |\space n \neq 2^m\}$$ is not regular using Myhill-Nerode is easy: Let $$i, j\in \mathbb{N}.i\neq j.$$ It follows $$1^{2^i}\nsim 1^{2^j}$$ because $$1^{2^i}0^{i}\notin L$$ but $$1^{2^j}0^{i}\in L$$. Therefore $$L$$ has an infinite amount of Myhill-Nerode equivalence classes and is not regular. But how do I show this using the general version of the pumping lemma for regular languages? https://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages#General_version_of_pumping_lemma_for_regular_languages