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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
	public static interface ICommon {
		public static final int BASE_DEF = 1000000007;
		public static final int CAPACITY = 100001;
	}
	
	//-----------------------------modulo calculate-------------------------------------
	public static class ModInt implements Cloneable, ICommon {
		private static Map<Integer,ModInt> instance = new HashMap<Integer,ModInt>();
		
		public static ModInt getInstance(int mod, int cap) {
			if(instance.containsKey(mod)){ 
				return instance.get(mod);
			} else {
				ModInt mi = new ModInt(mod,cap);
				instance.put(mod, mi);
				return mi;
			}
		}
		
		protected int mod = BASE_DEF;
		protected int capacity = CAPACITY;

		private ModInt(int m) {
			mod = m;
			initF();
		}
		private ModInt(int m, int cap) {
			mod = m;
			capacity=cap;
			initF();

		}
		
		public int modulo(long v) {
			return (int)(v%mod);
		}
		
		public int add(int a, int b) {
			return modulo(a + b);
		}
		
		public int sub(int a, int b) {
			return add(a, mod - b);
		}
		
		public int multiple(int a, int b) {
			return modulo((long)a * modulo(b));
		}
		
		public int divideF(int a, int fn) {
			if(fn<=capacity) {
				return multiple(a, getFInv(fn));
			}else{
				return divide(a, getF(fn));
			}
		}
		
		public int divide(int a, int b) {
			return multiple(a, power(b, mod-2));
		}

		public int power(int a, int b) {
			int ret = 1;
			for (int bitMask = 1; bitMask<=b; bitMask<<=1) {
				if ( (b & bitMask) != 0 ) ret = multiple(ret, a);
				a = multiple(a, a);
			}
			return ret;
		}

		//------------------Factorial--------------------
		private int[] Farray = null;;
		private int[] FInvarray = null;

		protected void initF() {
			if(Farray != null) return;
			Farray = new int[capacity+1];
			FInvarray = new int[capacity+1];
			for(int n=0; n<Farray.length; n++) {
				Farray[n] = (n==0) ? 1 : multiple(n, Farray[n-1]);
				FInvarray[n] = divide(1, Farray[n]);
			}
		}
		
		public int getF(int n) {
			return Farray[n];
		}

		public int getFInv(int n) {
			return FInvarray[n];
		}

		//------------------Permutation--------------------
		public int getP(int n, int r) {
			return calcP(n, r);
		}
		
		protected int calcP(int n, int r) {
			if ( n < 0 || r < 0 || n < r ) throw new IllegalArgumentException("n=" +n+ ",r=" +r);
			if ( n <= 1 || r == 0) return 1;
			if ( r == 1 ) return n;
			return divideF(getF(n), n-r);
			
		}
		//------------------Combination--------------------

		public int getC(int n, int r) {
			return calc(n,r);
		}
		
		public int getH(int n, int r) {
			return calc(n+r-1, r);
		}
		
		protected int calc(int n, int r) {
			if(n < 0 || r < 0 || n < r) throw new IllegalArgumentException("n=" +n+ ",r=" +r);
			if(n == 0 || n == 1) return 1;
			if(n - r < r) r = n - r;
			return divideF(divideF(getF(n), r),n-r);
		}
	}

	//-------------------------------------------------------------------------
	private int mod = ICommon.BASE_DEF;
	private ModInt modInt = null;
	public Main() {
		modInt = ModInt.getInstance(mod,ICommon.CAPACITY);
	}

	public void exec() {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] a = new int[n+1];
		for(int i=0; i<a.length; i++) {
			a[i] = scan.nextInt();
		}
		int[] search = new int[n+1];
		int l=0;
		int r=0;
		Arrays.fill(search, 0);
		for (int i=0; i<n+1; i++) {
			if(search[a[i]-1] != 0) {
				l = search[a[i]-1];
				r = i+1;
				break;
			} 
			else search[a[i]-1] = i+1;
		}
		PrintWriter out = new PrintWriter(System.out);
		
		for (int k=1; k<=n+1; k++) {
			int full = modInt.getC(n+1, k);
			int duplicate = 0;
			if (l-1+n+1-r >= k-1) {
				duplicate = modInt.getC(l-1+n+1-r,k-1);
			}
			out.println(modInt.sub(full,duplicate));
			
		}
		out.flush();
		scan.close();
	}

	public static void main(String[] args) {
//		long time = System.currentTimeMillis();
		new Main().exec();
//		System.out.println(System.currentTimeMillis() - time);
	}
}