Deal Into Consecutive Sets

Medium

There are cards on the table, each with a number: cards[i] is the number on card i. Several cards may show the same number. You need to split all the cards into sets of exactly size cards so that each set holds consecutive numbers: x, x + 1, …, x + size - 1. Every card must go into exactly one set. Return True if such a split is possible and False otherwise.

Example 1

cards=[5, 3, 4, 4, 6, 5], size=3 → True

The cards split into the sets [3, 4, 5] and [4, 5, 6].

Example 2

cards=[1, 2, 4, 5], size=2 → True

[1, 2] and [4, 5] work: each set holds consecutive values.

Example 3

cards=[2, 3, 3, 4], size=2 → True

The 2 can only go with a 3, which leaves 3 and 4, also a valid set. The answer is True.

Constraints

1 ≤ len(cards) ≤ 10⁵
0 ≤ cards[i] ≤ 10⁹
1 ≤ size ≤ len(cards)

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Topics

Greedy Array Hash Table Sorting

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Input

cards=[5, 3, 4, 4, 6, 5], size=3

Expected

True

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