If a function f satisfies f( m + n )=f( m )+f( n ) for all m, n ∈ N and f(1)=1, then the largest natural number λ such that Σ_k=1^2022 f(λ+k)…

If a function $\displaystyle f$ satisfies $\displaystyle f(\mathrm{~m}+\mathrm{n})=f(\mathrm{~m})+f(\mathrm{n})$ for all $\displaystyle \mathrm{m}, \mathrm{n} \in \mathrm{N}$ and $\displaystyle f(1)=1$, then the largest natural number $\displaystyle \lambda$ such that $\displaystyle \sum_{k=1}^{2022} f(\lambda+k) \leq(2022)^2$ is equal to $\displaystyle \_\_\_\_$.