Ball Distribution

There are B balls, numbered 1 to B. The Chef is distributing all B balls among B children, giving one ball to every child. He does that iteratively. In the first pass, starting from the first ball he gives out every alternate ball, in the second pass, he gives out every third ball starting from the first remaining ball, in the kth pass, he gives out every (k+1)th ball. He does this until all the b