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With the idea of normal family we study the uniqueness of meromorphic functions $f$ and $g$ when $f^n(f^{(k)})^m-p$ and $g^n(g^{(k)})^m-p$ share two values, where $p$ is any nonzero polynomial. The result of this paper significantly improves and generalizes the result due to A. Banerjee and S. Majumder (2018).