Lower bound of minimum eigenvalue of positive definite matrix using the smallest off-diagonal element and largest diagonal element

Question

Consider an $K \times K$ symmetric positive definite matrix $A$ that has the following properties

1. All of its elements are nonnegative and within $0$ and $1$, i.e. $0 < A_{ij} < 1$
2. The smallest element of all its diagonal elements is $d$, i.e. $d = \min_{i} A_{ii}$
3. The largest element of all its off-diagonal elements is $r$, i.e. $r = max_{i, j} A_{ij}$ for all $i \neq j$
4. $d > r$
5. Let $\lambda_K$ be the smallest eigenvalue of $A$.

Is there a way to give a lower bound of the minimum eigenvalue of this matrix in terms of $r$ and $d$, like $\lambda_K \ge C\cdot(d - r)$, where $C$ is a constant?

Any help would be appreciated.