My solution passed both visible test sets, but I got a "TIME_LIMIT_EXCEEDED" 
error on the hidden one. As far as I can tell, I did exactly what was described 
to solve test set 3 in the analysis. What did I do wrong?

(Python 3)

for T in range(int(input())):
    N, L = list(map(int, input().split()))
    C = list(map(int, input().split()))

    if 100 % N != 0:
        remaining = N - sum(C)
        counts = C + [0 for i in range(remaining)]

        needed = []
        for cnt in counts:
            num = cnt
            while num * 100 / N - int(num * 100 / N) < 0.5:
                num += 1
            needed.append(num - cnt)

        needed, counts = list(map(list, zip(*sorted(zip(needed, counts)))))

        for i in range(len(counts)):
            if needed[i] <= remaining:
                counts[i] += needed[i]
                remaining -= needed[i]
        counts[-1] += remaining
        
        result = []
        for cnt in counts:
            percentage = cnt * 100 / N
            if percentage - int(percentage) < 0.5:
                result.append(int(percentage))
            else:
                result.append(int(percentage) + 1)

        print('Case #' + str(T + 1) + ': ' + str(sum(result)))

    else:
        print('Case #' + str(T + 1) + ': 100')

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