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.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.net.ConnectException;
import java.rmi.dgc.Lease;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;

import static java.util.Comparator.*;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
		main.out.close();
	}

	// ======================================================================
	int[] P;
	public void solve() {
		int N = ni();
		P = new int[N];
		Arrays.fill(P, -1);
		int a, l = -1, r = -1;
		for (int i = 0; i < N; i++) {
			a = ni() - 1;
			if(P[a] != -1) {
				l = P[a];
				r = N - i;
			} else {
				P[a] = i;
			}
		}
//		out.println("l = " + l + "  r = " + r);
		COMinit();
		out.println(N);
		long ans, all, dd;
		for (int i = 2; i <= N+1; i++) {
			all = COM(N+1, i);
			dd = COM(l+r, i-1);
			ans = (all + MOD - dd) % MOD;
			out.println(ans);
		}
	}
	int MAX = 510000;
	int MOD = (int) (1e9) + 7;;
	long[] fac, finv, inv; // a! (fac[a])   (a!)の-1乗 (finv[a])

	// テーブルを作る前処理　→　これを呼んでから COM() を呼ぶ
	void COMinit() {
		fac = new long[MAX];
		finv = new long[MAX];
		inv = new long[MAX];
		fac[0] = fac[1] = 1;
		finv[0] = finv[1] = 1;
		inv[1] = 1;
		for (int i = 2; i < MAX; i++) {
			fac[i] = fac[i - 1] * i % MOD;
			inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
			finv[i] = finv[i - 1] * inv[i] % MOD;
		}
	}

	// 組み合わせの数を計算する(a個の中からb個を選ぶ）
	long COM(int n, int k) {
		if (n < k)
			return 0;
		if (n < 0 || k < 0)
			return 0;
		return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
	}
	// ------------------------------------------
	// ライブラリ
	// ------------------------------------------
	// Print
	private PrintWriter out = new PrintWriter(System.out);

	// Scanner
	private FastScanner scan = new FastScanner();

	int ni() {
		return scan.nextInt();
	}

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

	int[][] ni(int y, int x) {
		int[][] a = new int[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = ni();
			}
		}
		return a;
	}

	long nl() {
		return scan.nextLong();
	}

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

	long[][] nl(int y, int x) {
		long[][] a = new long[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = nl();
			}
		}
		return a;
	}

	String ns() {
		return scan.next();
	}

	String[] ns(int n) {
		String[] a = new String[n];
		for (int i = 0; i < n; i++) {
			a[i] = ns();
		}
		return a;
	}

	String[][] ns(int y, int x) {
		String[][] a = new String[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = ns();
			}
		}
		return a;
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}

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