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