Suppose n people are arranged in a circle. Number the people from 1 to n. in the clockwise order. We are given an integer ,m <= n. Beginning with the person with designated number 1, we proceed around the circle (in clockwise order) removing every mth person. After each person is removed, counting continues around the circle that remains. This process continues until all the n people have been removed. . The .m-permutation is defined as the order in which the people have been removed. As an example, if n = 7, m = 3, then the 3 - permutation is 3,6,2,7,5,1,4. Give an O(n log n) time algorithm which given m and n outputs the m- permutation.
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