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.

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.

Examples

Input

3
1 2 1 3


Output

3
5
4
1


Input

1
1 1


Output

1
1


Input

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


Output

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

import java.util.*;
import java.io.*;

public class Main {
	static int mod = (int) 1e9 + 7;

	public static void main(String[] args) {
		FastScanner fs = new FastScanner(System.in);
		int n = fs.nextInt();
		int a[] = fs.nextIntArray(n+1);
		int s[] = new int[n+1];
		Arrays.fill(s, -1);
		int p = -1, q = -1;
		for(int i=0;i<n+1;i++) {
			if(s[a[i]]==-1)s[a[i]]=i;
			else {
				p = s[a[i]];
				q = i;
			}
		}
		
		pre_factrials(n+1);
		
		StringBuilder sb = new StringBuilder();
		for(int k=1;k<=n+1;k++) {
			long t1 = fastFermatComb(n+1, k);
			long t2 = 0;
			if(p+n-q>=k-1) {
				t2 = fastFermatComb(p+n-q,k-1);
			}
			
			long ans = sub(t1, t2);
			sb.append(ans + "\n");
		}
		System.out.println(sb.toString());
	}
	//Fast Fermat Combination
	static long factorials[];

	static void pre_factrials(int n) {
		factorials = new long[n + 1];
		factorials[0] = 1;
		for (int i = 0; i < n; i++) {
			factorials[i + 1] = mul(i + 1, factorials[i]);
		}
	}

	static long fastFermatComb(long a, long b) {
		if (factorials.length == 0)
			System.err.println("error : factorials has not been culculated!! do [pre_factorial] method");
		long af = factorials[(int) a];
		long bf = factorials[(int) b];
		long abf = factorials[(int) (a - b)];
		long res = af * modpow(bf, mod - 2) % mod * modpow(abf, mod - 2) % mod;
		return res;
	}
	
	//MOD culculations
	static long plus(long x, long y) {
		x %= mod;
		y %= mod;
		long res = (x + y) % mod;
		return res;
	}

	static long sub(long x, long y) {
		x %= mod;
		y %= mod;
		long res = (x - y + mod) % mod;
		return res;
	}

	static long mul(long x, long y) {
		x %= mod;
		y %= mod;
		long res = x * y % mod;
		return res;
	}

	static long div(long x, long y) {
		x %= mod;
		y %= mod;
		long res = x * modpow(y, mod - 2) % mod;
		return res;
	}

	//modの元での高速pow()
	static long modpow(long a, long p) {
		if (p == 0)
			return 1;
		if (p % 2 == 0) {
			long halfP = p / 2;
			long root = modpow(a, halfP);
			return root * root % mod;
		} else
			return a * modpow(a, p - 1) % mod;
	}


}

//高速なScanner
class FastScanner {
	private BufferedReader reader = null;
	private StringTokenizer tokenizer = null;

	public FastScanner(InputStream in) {
		reader = new BufferedReader(new InputStreamReader(in));
		tokenizer = null;
	}

	public String next() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

	public String nextLine() {
		if (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken("\n");
	}

	public long nextLong() {
		return Long.parseLong(next());
	}

	public int nextInt() {
		return Integer.parseInt(next());
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}
}