Prove any positive integer can be expressed as a combination of distinct powers of $\pm4^n$ and $\pm3^{2m-1}$

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Prove that any positive integer can be expressed as a combination of distinct powers of $\pm4^n$ and $\pm3^{2m+1}$(where m,n are integers). Like $33=4^3-4^0-3^3-3^1$