1. Explain how to solve the following two problems using heaps. (No credit if you're not using heaps!) First, give an O(nlogk) algorithm to merge k sorted lists with n total elements into one sorted list. Second, say that a list of numbers is k-close to sorted if each number in the list is less than k positions from its actual place in the sorted order. (Hence, a list that is 1-close to sorted is actually sorted.) Give an O(nlogk) algorithm for sorting a list of n numbers that is k-close to sorted