$C^2$ interpolation with range restriction

Given $-\infty< \lambda < \Lambda \infty$ , $E \subset \mathbb{R}^n$ finite, and $f\colon E \to \[\lambda,\Lambda]$ how can we extend $f$ to a $C^m(\mathbb{R}^n)$ function $F$ such that $\lambda\leq F \leq \Lambda$ $|F|\_{C^m(\mathbb{R}^n)}$ is within constant multiple of the least possible, with depending only on $m$ $n$? In this paper, provide solution problem for case ${m = 2}$. Specifically, construct (parameter-dependent, nonlinear) $C^2(\mathbb{R}^n)$ extension operator preserves range $\[\lambda,\Lambda]$, an efficient algorithm compute using $O(N\log N)$ operations, where $N #(E)$ .