Find the range of kkk such that the system ∣x−1∣≤2|x-1| \leq 2∣x−1∣≤2 and ∣x−k∣≤1|x-k| \leq 1∣x−k∣≤1 has at least one solution.
k∈[0,2]k \in [0, 2]k∈[0,2]
k∈[−2,2]k \in [-2, 2]k∈[−2,2]
k∈[−1,3]k \in [-1, 3]k∈[−1,3]
k∈[−2,4]k \in [-2, 4]k∈[−2,4]