let's consider a set that will call sigma which consists of an integer sequence with the following properties a0=1 am=n a0<a1<a2......<am-1<am quelque soit k apartient [1,m] il existe i&j apartiennent [0,k-1]such that ak=ai+aj given an integer n as input your program should construst a,d outputs a sequence of inegers with minimal length satisfying the properties above for n note thet there can be more than one sequence satisfying the properties your program should output the one with the maximal sum Input: the input consists of 100 test cases text cases are stored in an input file named sigma in .eatch test case in the file is stored in a separate line and the number -1 marks the end of the input file Output: the output file file should be named sigma out and should follow this organization each test case output consits of a sequence of integers separated by one blank Sample Input:
3
4
9
77
80
87
99
-1
Sample Output:
1 2 3
1 2 4
1 2 4 8 9
1 2 4 8 9 17 34 68 77
1 2 4 8 16 32 64 80
1 2 4 8 16 24 28 29 58 87
1 2 4 8 16 32 33 66 99