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
/**
 * Created at 00:38 on 2019-09-03
 */

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

public class Main {

  static FastScanner sc = new FastScanner();
  static Output out = new Output(System.out);

  static final int[] dx = {0, 1, 0, -1};
  static final int[] dy = {-1, 0, 1, 0};

  static final long MOD = (long) (1e9 + 7);
  static final long INF = Long.MAX_VALUE / 2;

  static final int e5 = (int) 1e5;

  public static class Solver {
    public Solver() {

      int N = sc.nextInt();

      int[] A = new int[N+1];
      int[] B = new int[N];
      Arrays.fill(B, -1);
      int[] same = new int[2];
      for (int i=0; i<N+1; i++) {
        A[i] = sc.nextInt() - 1;
        if (B[A[i]] == -1) {
          B[A[i]] = i;
        } else {
          same[0] = B[A[i]];
          same[1] = i;
          A[i] = -2;
        }
      }

      new Mod(N+1);

      for (int i=1; i<=N+1; i++) {

        long c = Mod.comb(N+1 - (same[1] - same[0] + 1), i-1);

        long ans = Mod.add(Mod.comb(N-1, i), //二つとも選ばない
                   Mod.comb(N-1, i-2), //二つとも選ぶ
                   c, //片方を選んで他は二つの外側のみから選ぶ
                   Mod.mul(Mod.sub(Mod.comb(N-1, i-1), c), 2)); //片方を撰んで二つの間から1つ以上選ぶ

        out.println(ans);

      }

    }


    public static class Mod {

      static final long MOD = (long) (1e9 + 7);

      public static long[] fact;

      public Mod(int n) {
        fact = new long[n+1];
      }

      public Mod(long n) {
        fact = new long[(int)n+1];
      }

      public static long comb(long n, long r) {
        if (r < 0 || r > n) return 0;
        return (((factorial(n) * factorialInverse(r)) % MOD) * factorialInverse(n - r)) % MOD;
      }

      public static long factorial(long n) {
        if (n == 0) return 1;
        if (fact[(int) n] == 0) {
          return fact[(int) n] = (n * factorial(n - 1)) % MOD;
        } else {
          return fact[(int) n];
        }
      }

      public static long factorialInverse(long n) {
        return inverse(factorial(n));
      }

      public static long inverse(long n) {
        return power(n, MOD - 2);
      }

      public static long power(long a, long b) {
        if (b == 0) return 1;

        if (b % 2 == 0) {
          long p = power(a, b / 2);
          return (p * p) % MOD;
        } else {
          return (a * power(a, b - 1)) % MOD;
        }
      }

      public static long add(long... a) {
        long ans = 0;
        for (int i=0; i<a.length; i++) {
          ans = (ans + a[i]) % MOD;
        }
        return ans;
      }

      public static long sub(long a, long b) {
        return (a - b + MOD) % MOD;
      }

      public static long mul(long... a) {
        long ans = 1;
        for (int i=0; i<a.length; i++) {
          ans = (ans * a[i]) % MOD;
        }
        return ans;
      }

      public static long div(long a, long b) {
        return (a * Mod.inverse(b)) % MOD;
      }

    }
  }

  public static void main(String[] args) {
    new Solver();
    out.flush();
  }

  static 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;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
    }

    public boolean hasNext() {
      skipUnprintable();
      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() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int N, boolean oneBased) {
      if (oneBased) {
        int[] array = new int[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      } else {
        int[] array = new int[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextInt();
        }
        return array;
      }
    }

    public long[] nextLongArray(int N, boolean oneBased) {
      if (oneBased) {
        long[] array = new long[N + 1];
        for (int i = 1; i <= N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      } else {
        long[] array = new long[N];
        for (int i = 0; i < N; i++) {
          array[i] = sc.nextLong();
        }
        return array;
      }
    }
  }

  static class Output extends PrintWriter {

    public Output(PrintStream ps) {
      super(ps);
    }

    public void print(int[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(long[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(String[] a, String separator) {
      for (int i = 0; i < a.length; i++) {
        if (i == 0) print(a[i]);
        else print(separator + a[i]);
      }
      println();
    }

    public void print(ArrayList a, String separator) {
      for (int i = 0; i < a.size(); i++) {
        if (i == 0) print(a.get(i));
        else print(separator + a.get(i));
      }
      println();
    }
  }

}
