Need the proof for this question please

2. Consider the following variation of the Mergesort algorithm. Instead of partitioning the input array into two roughly ba anced parts, we will partition it into m parts. Let m-Vi, and let the m subarravs have the sae size. The sorted subar rays are merged using a priority queue implemented as a binary heap (hence, insertions and deletions are performed in logarith- mic time, with respect to the size of the queue). Prove that the running time of this variant is O(n log n log log n. Hint: show that the recursion tree has O(log log n) levels.] 2. Consider the following variation of the Mergesort algorithm. Instead of partitioning the input array into two roughly ba anced parts, we will partition it into m parts. Let m-Vi, and let the m subarravs have the sae size. The sorted subar rays are merged using a priority queue implemented as a binary heap (hence, insertions and deletions are performed in logarith- mic time, with respect to the size of the queue). Prove that the running time of this variant is O(n log n log log n. Hint: show that the recursion tree has O(log log n) levels.]