一、题目回顾
题目链接：Anti-prime Sequences
Description
Given a sequence of consecutive integers n,n+1,n+2,...,m, an anti-prime sequence is a rearrangement of these integers so that each adjacent pair of integers sums to a composite (non-prime) number. For example, if n = 1 and m = 10, one such anti-prime sequence is 1,3,5,4,2,6,9,7,8,10. This is also the lexicographically first such sequence.
We can extend the definition by defining a degree danti-prime
sequence as one where all consecutive subsequences of length 2,3,...,d
sum to a composite number. The sequence above is a degree 2 anti-prime
sequence, but not a degree 3, since the subsequence 5, 4, 2 sums to 11.
The lexicographically .rst degree 3 anti-prime sequence for these
numbers is 1,3,5,4,6,2,10,8,7,9.
一个由连续的整数（n,n+1,n+2,…,m）组成的序列，an anti-prime sequence就是这些整数的重新排列，使每一对相邻的整数与一个复合(非素数)数相加。例如，如果n = 1和m = 10，一个这样的anti-prime sequence就是1 3 5 4 2 6 9 7 8 10。 This is also the lexicographically first such sequence.
我们可以通过定义一个danti - prime sequence来扩展这个定义，它的长度为2,3，…，d和一个复合数。上面的序列是2次反质数序列，而不是3次，因为子序列5、4、2和11。字母顺序进行的第3次反质数序列为1 3 5 4 6 2 10 8 7 9。
Input
Input will consist of multiple input sets. Each set will consist of three integers, n, m, and d on a single line. The values of n, m and d will satisfy 1 <= n < m <= 1000, and 2 <= d <= 10. The line 0 0 0 will indicate end of input and should not be processed.
Output
For each input set, output a single line consisting of a comma-separated list of integers forming a degree danti-prime sequence (do not insert any spaces and do not split the output over multiple lines). In the case where more than one anti-prime sequence exists, print the lexicographically first one (i.e., output the one with the lowest first value; in case of a tie, the lowest second value, etc.). In the case where no anti-prime sequence exists, output “No anti-prime sequence exists.”
Sample Input
1 10 2
1 10 3
1 10 5
40 60 7
0 0 0
Sample Output
1,3,5,4,2,6,9,7,8,10
1,3,5,4,6,2,10,8,7,9
No anti-prime sequence exists.
40,41,43,42,44,46,45,47,48,50,55,53,52,60,56,49,51,59,58,57,54
题意：求n到m的一个排列，满足任意连续的k(2<=k<=d)个数的和都不为素数。
二、解题思路