You are given an integer sequence of length n+1, a_1,a_2,...,a_{n+1}, which consists of the n integers 1,...,n.
It is known that each of the n integers 1,...,n appears at least once in this sequence.
For each integer k=1,...,n+1, find the number of the different subsequences (not necessarily contiguous) of the given sequence with length k, modulo 10^9+7.

-----Notes-----
- If the contents of two subsequences are the same, they are not separately counted even if they originate from different positions in the original sequence.
- A subsequence of a sequence a with length k is a sequence obtained by selecting k of the elements of a and arranging them without changing their relative order. For example, the sequences 1,3,5 and 1,2,3 are subsequences of 1,2,3,4,5, while 3,1,2 and 1,10,100 are not.

-----Constraints-----
- $1 \leq n \leq 10^5$
- $1 \leq a_i \leq n$
- Each of the integers 1,...,n appears in the sequence.
- n and a_i are integers.

-----Input-----
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_{n+1}

-----Output-----
Print n+1 lines.
The k-th line should contain the number of the different subsequences of the given sequence with length k, modulo 10^9+7.

-----Sample Input-----
3
1 2 1 3

-----Sample Output-----
3
5
4
1

There are three subsequences with length 1: 1 and 2 and 3.
There are five subsequences with length 2: 1,1 and 1,2 and 1,3 and 2,1 and 2,3.
There are four subsequences with length 3: 1,1,3 and 1,2,1 and 1,2,3 and 2,1,3.
There is one subsequence with length 4: 1,2,1,3.

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