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Gwen's Gift Gwen loves most numbers. In fact, she loves every number that is not a multiple of n (she really hates the number n). For her friends' birthdays this year, Gwen has decided to draw each of them a sequence of n - flowers. Each of the flowers will contain between 1 and n flower petals (inclusive). Because of her hatred of multiples of n, the total number of petals in any non-empty contiguous subsequence of flowers cannot be a multiple of n. For example, if n = 5, then the top two paintings are valid, while the bottom painting is not valid since the second, third and fourth flowers have a total of 10 petals. (The top two images are Sample Input 3 and 4.) Gwen wants her paintings to be unique, so no two paintings will have the same sequence of flowers. To keep track of this, Gwen recorded each painting as a sequence of n - 1 numbers specifying the number of petals in each flower from left to right. She has written down all valid sequences of length n-1 in lexicographical order. A sequence ai ,a2, , an-l s lexicographically smaller than bim, bn-l if there exists an index k such that ai = bi for i