JOIN

 Problem Statement

Problem Statement for CliqueParty

### Problem Statement

A set of positive integers is called k-smooth if each pair (A,B) of elements of the set satisfies A <= k * B. For example, the set {3,4,7,9} is 3-smooth but the set {30,60,100} is not: 100 is strictly more than 3 * 30.

Hero likes some sets of integers. In order to determine whether he likes a set S, Hero uses the following procedure:
1. Form a new set D of pairwise differences of elements in S. In other words: for each pair of elements A, B in S, put the number |A-B| into D.
2. Hero likes the original set S if and only if the new set D is k-smooth.
You are given a int[] a containing a set of distinct integers. You are also given the int k Hero uses while determining whether he likes a set of integers.

Select the largest subset of a Hero likes. Return the number of elements in that subset.

### Definition

 Class: CliqueParty Method: maxsize Parameters: int[], int Returns: int Method signature: int maxsize(int[] a, int k) (be sure your method is public)

### Constraints

-Number of elements in a will be between 2 and 50, inclusive.
-Each elements in a will be between 1 and 1,000,000,000, inclusive.
-All elements in a will be distinct.
-k will be between 1 and 1,000,000,000, inclusive.

### Examples

0)

 `{1,2,3}` `2`
`Returns: 3`
 Hero likes the entire set a.
1)

 `{1,2,3}` `1`
`Returns: 2`
 Here, Hero does not like the entire set a, but he does like, for example, the subset {1,3}.
2)

 `{4,10,5,6}` `2`
`Returns: 3`
3)

 `{1,2,3,4,5,6}` `3`
`Returns: 4`
4)

 `{10,9,25,24,23,30}` `7`
`Returns: 4`

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This problem was used for:
Single Round Match 684 Round 1 - Division I, Level One