找到一组数字的最大子集，以使任意两个数字之和不能被给定数字整除

我正在尝试解决如下所述的Hackerrank问题不可分割子集：

我尝试了以下解决方案（适用于示例测试用例）：

# The lines below are for Hackerrank submissions
# n, k = map(int, raw_input().strip().split(' '))
    # a = map(int, raw_input().strip().split(' '))

n = 4
k = 3
a = [1, 7, 2, 4]

while True:
    all_pairs = [(a[i],a[j]) for i in range(len(a)) for j in range(i+1,len(a))]
    tested_pairs = {pair: (pair[0] + pair[1]) % k != 0 for pair in all_pairs}
    disqualified_pairs = {key: value for key, value in tested_pairs.iteritems() if not value}.keys()
    if not disqualified_pairs:
        break
    occurrences = list(sum(disqualified_pairs, ()))
    counts = map(lambda x: occurrences.count(x), a)
    index_remove = counts.index(max(counts))
    a.remove(index_remove)

print len(a)

我要做的是确定“违规”对，并删除a其中最频繁发生的元素，直到没有“违规”对为止。

但是，对于大多数测试用例，我都会遇到“运行时错误”：

Presumably the algorithm above works in this simple case where only one number (the number 2) needs to be removed, but fails in more complicated test cases. Can anyone see what is wrong with it?

UPDATE

Following poke's suggestion to test k = 2 and a = [1, 2, 3], I made the following modifications:

n = 4
k = 2
a = [1, 2, 3]

while True:
    all_pairs = [(a[i],a[j]) for i in range(len(a)) for j in range(i+1,len(a))]
    disqualified_pairs = [pair for pair in all_pairs if (pair[0] + pair[1]) % k == 0]
    if not disqualified_pairs:
        break
    offending_numbers = sum(disqualified_pairs, ())   # 'Flatten' the disqualified pairs into a single list
    counts = {el: offending_numbers.count(el) for el in set(offending_numbers)}     # Count occurrences of each offending number
    number_to_remove = max(counts, key=counts.__getitem__)
    a.remove(number_to_remove)

print len(a)

The resulting a is [2, 3] and contains two elements as expected. I've also checked that it still works for the original example. However, I am still getting a "Segmentation Fault" on some of the test cases:

According to https://www.hackerrank.com/challenges/pairs/forum/comments/9154, segmentation faults typically occur because of invalid memory access (array indices which don't exist, etc.). I still haven't managed to find any other test cases, though, where the algorithm fails. Any ideas?