Problem:
Score : 600 points

Problem Statement

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 1

3
1 2 1 3

Sample Output 1

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.

Sample Input 2

1
1 1

Sample Output 2

1
1

There is one subsequence with length 1: 1.

There is one subsequence with length 2: 1,1.

Sample Input 3

32
29 19 7 10 26 32 27 4 11 20 2 8 16 23 5 14 6 12 17 22 18 30 28 24 15 1 25 3 13 21 19 31 9

Sample Output 3

32
525
5453
40919
237336
1107568
4272048
13884156
38567100
92561040
193536720
354817320
573166440
818809200
37158313
166803103
166803103
37158313
818809200
573166440
354817320
193536720
92561040
38567100
13884156
4272048
1107568
237336
40920
5456
528
33
1

Be sure to print the numbers modulo 10^9+7.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Reflection.Emit;
using System.Runtime.InteropServices;
using System.Text;
using System.Threading.Tasks;
using System.Xml;

namespace ConsoleApp1
{
    public class Ring
    {
        private int[] ary;
        private int first;
        private int last;
        public Ring( int size )
        {
            ary = new int[size];
            last = size / 2;
            first = size / 2-1;
        }

        public void AddLast(int i)
        {
            ary[last++] = i;
        }

        public void AddFirst(int i)
        {
            ary[first--] = i;
        }

        public void Reverse()
        {
            Console.WriteLine(string.Join(" ", ary.Reverse()));
        }

        public void Print()
        {
            Console.WriteLine(string.Join(" ", ary));
        }
    }

    class Program
    {
        static void Main(string[] args)
        {
            //string str = Console.ReadLine();
            //Main2(str);
            //MainSS(str);
//            MainC();
            MainD();
        }
        /// <summary>
        /// 引数 n の階乗 n! を計算します。
        /// </summary>
        /// <param name="n">自然数 n</param>
        /// <returns>n の階乗</returns>
        public static BigInteger Factorial(BigInteger n)
        {
            if (n < 0)
            {
                throw new ArgumentOutOfRangeException();
            }
            BigInteger y = 1;
            for (var i = n; i > 0; --i)
            {
                y *= i;
            }
            return y;
        }

        static void MainD()
        {

            var n = int.Parse(Console.ReadLine());
            var ary = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Console.WriteLine(n);

            int two = n;
            for (int i = 0; i < n - 1; i++)
            {
                for (int k = i+1; k < n; k++)
                {
                    if (ary[i] == ary[k])
                    {
                        two = k;
                        goto end;
                    }
                }
            }
            end:

            for (int i = 2; i < n+1; i++)
            {
                //(n+1)C(i)
                if (n + 1 - two - i >= 0)
                    Console.WriteLine((Factorial(n + 1) / (Factorial(i) * Factorial(n + 1 - i))
                                      - Factorial(n + 1 - two) / (Factorial(i) * Factorial(n + 1 - two - i)))
                                      % (1000000007));
                else
                    Console.WriteLine(Factorial(n + 1) / (Factorial(i) * Factorial(n + 1 - i)) % (1000000007) );

            }
            Console.WriteLine(1);
        }

        static void MainC()
        {
            var n = int.Parse(Console.ReadLine());
            var ary = Console.ReadLine().Split().Select(int.Parse).ToArray();
            
            Ring r = new Ring(ary.Length);
            for (int i = 0; i < n; i++)
            {
                if(i % 2 == 0)
                    r.AddLast(ary[i]);
                else
                    r.AddFirst(ary[i]);
            }
            if(ary.Length % 2 == 0)
                r.Print();
            else
                r.Reverse();


        }

        static void MainSS(string str)
        {
            for (int i = 2; i < str.Length; i+=2)
            {
                if (JudgeGu(str.Substring(0, str.Length - i)))
                {
                    Console.WriteLine(str.Length - i);
                    break;
                }
            }
        }

        static bool JudgeGu(string str)
        {
            if (str.Length % 2 != 0) return false;

            string sub = str.Substring(0, str.Length / 2);
            return (sub + sub) == str;
        }

        static void Main2(string str)
        {
            var kakaku = str.Split().Select(int.Parse).ToArray();
            Array.Sort(kakaku);
            Console.WriteLine(kakaku[0] + kakaku[1]);
        }
    }
}