Run-length encoding is a compression algorithm that allows for an integer array nums with many segments of consecutive repeated numbers to be represented by a (generally smaller) 2D array encoded. Each encoded[i] = [vali, freqi] describes the ith segment of repeated numbers in nums where vali is the value that is repeated freqi times.

• For example, nums = [1,1,1,2,2,2,2,2] is represented by the run-length encoded array encoded = [[1,3],[2,5]]. Another way to read this is "three 1's followed by five 2's".

The product of two run-length encoded arrays encoded1 and encoded2 can be calculated using the following steps:

1. Expand both encoded1 and encoded2 into the full arrays nums1 and nums2 respectively.
2. Create a new array prodNums of length nums1.length and set prodNums[i] = nums1[i] * nums2[i].
3. Compress prodNums into a run-length encoded array and return it.

You are given two run-length encoded arrays encoded1 and encoded2 representing full arrays nums1 and nums2 respectively. Both nums1 and nums2 have the same length. Each encoded1[i] = [vali, freqi] describes the ith segment of nums1, and each encoded2[j] = [valj, freqj] describes the jth segment of nums2.

Return the product of encoded1 and encoded2.

Note: Compression should be done such that the run-length encoded array has the minimum possible length.

 

Example 1:

Input: encoded1 = [[1,3],[2,3]], encoded2 = [[6,3],[3,3]]
Output: [[6,6]]
Explanation: encoded1 expands to [1,1,1,2,2,2] and encoded2 expands to [6,6,6,3,3,3].
prodNums = [6,6,6,6,6,6], which is compressed into the run-length encoded array [[6,6]].

Example 2:

Input: encoded1 = [[1,3],[2,1],[3,2]], encoded2 = [[2,3],[3,3]]
Output: [[2,3],[6,1],[9,2]]
Explanation: encoded1 expands to [1,1,1,2,3,3] and encoded2 expands to [2,2,2,3,3,3].
prodNums = [2,2,2,6,9,9], which is compressed into the run-length encoded array [[2,3],[6,1],[9,2]].

 

Constraints:

• 1 <= encoded1.length, encoded2.length <= 105
• encoded1[i].length == 2
• encoded2[j].length == 2
• 1 <= vali, freqi <= 104 for each encoded1[i].
• 1 <= valj, freqj <= 104 for each encoded2[j].
• The full arrays that encoded1 and encoded2 represent are the same length.