You are given a list 'v' of numbers. This list may contain repeated numbers. Your objective is to create a new list that maintains the same elements in the same order as the original list. However, if a number appears more than 'k times in the original list, only the first 'k' occurences of that number will be included in the new list. Any additional instances of that number beyond the k-th occurrence will be discarded. Note that, if k equals 0, the resulting list would be empty.
Example: if v = [ 1, 3, 5, 3, 1, 3, 5, 3, 1 ] and k = 2, the function should output [ 1, 3, 5, 3, 1, 5 ].
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