Solve interval deletion and GCD subarray problems

1) Given n closed intervals [li, ri] on a number line, remove the fewest intervals so that among the remaining intervals there exists at least one interval that fully covers all other remaining intervals (i.e., there is [L, R] such that for every remaining [l, r], L <= l and r <= R). Return the minimum number of deletions required and describe an algorithm with time and space complexity. 2) Given an integer array nums and an integer k (maximum number of elements you may change within a chosen subarray), find the minimum length of a contiguous subarray such that, after modifying at most k elements inside that subarray to any positive integers of your choice, the subarray’s greatest common divisor is greater than 1. Return the minimal length and outline an efficient approach. Example: nums = [2, 2, 4, 9, 6], k = 1 -> output 1.