Use JAVA: Problem 1: Given k sorted arrays of size n, design an algorithm merge these arrays into a single sorted array of size kn? (Hint: A sorted array is a min heap. If you have k min heaps, can you find and delete the smallest number in each of them? If so, can you create another min heap with your k smallest numbers? In the new min heap with k numbers, can you sort the numbers? The time complexity of your solution should be O(nklogk).) Example: al - [e, 2, 4, 6], a2 [1, 5, 8, 10], a3 -[3, 7, 9, 20], Output: Merged array: [e 1 2 3 567 8 9 10 20] Problem 2: Sort a given random array of n numbers where each element is at most k index away from its position in the sorted array. (Hint: You could make min/max heaps using the first k+1 numbers and then 1- delete the root once 2- add the next element to the heap 3-Repeat 1 and 2 until you cover all the elements. The time complexity of your solution should be O(nlogk).) Example: Input: a -[2, 8, 0, 17, 5, 12], k - 2, (Hint: a number at index 4 in our sorted array, can be located in 2, 3, 4, 5, 6 indices in the given array.) Output: [e 2 5 8 12 17]