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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        D11 solver = new D11();
        solver.solve(1, in, out);
        out.close();
    }

    static class D11 {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int[] a = in.readIntArray(n + 1);

            int diff = 0;
            int[] pos = new int[n + 1];
            Arrays.fill(pos, -1);
            for (int i = 0; i < n + 1; i++) {
                if (pos[a[i]] != -1) {
                    diff = i - pos[a[i]];
                    break;
                }
                pos[a[i]] = i;
            }

            Combination c = new Combination(n + 1, MiscUtils.MOD7);
            Modulo m = new Modulo(MiscUtils.MOD7);
            out.printLine(n);
            for (int i = 2; i <= n + 1; i++) {
                long ans = 0;
                ans = m.add(ans, c.combMod(n - 1, i - 2));
                if (n - 1 >= i - 1) {
                    ans = m.add(ans, c.combMod(n - 1, i - 1));
                    ans = m.add(ans, c.combMod(n - 1, i - 1));
                }
                if (n - 1 - (diff - 1) >= i - 1) {
                    ans = m.sub(ans, c.combMod(n - 1 - (diff - 1), i - 1));
                }
                if (n - 1 >= i) {
                    ans = m.add(ans, c.combMod(n - 1, i));
                }
                out.printLine(ans);
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

        public void printLine(int i) {
            writer.println(i);
        }

    }

    static class MiscUtils {
        public static final int MOD7 = (int) (1e9 + 7);

    }

    static class Modulo {
        long m;

        public Modulo(long m) {
            this.m = m;
        }

        public long add(long a, long b) {
            return (a + b) % m;
        }

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

        public long mlt(long a, long b) {
            return (a * b) % m;
        }

        public long rev(long a) {
            return pow(a, m - 2);
        }

        public long pow(long a, long x) {
            long ans = 1 % m;
            while (x > 0) {
                if ((x & 1) != 0) {
                    ans = (ans * a) % m;
                }
                x >>= 1;
                a = (a * a) % m;
            }
            return ans;
        }

    }

    static class Combination {
        Modulo modulo;
        long[] nors;
        long[] revs;

        public Combination(int n, long m) {
            nors = new long[n + 1];
            revs = new long[n + 1];
            modulo = new Modulo(m);

            nors[0] = 1;
            for (int i = 1; i <= n; i++) {
                nors[i] = modulo.mlt(nors[i - 1], i);
            }

            revs[n] = modulo.rev(nors[n]);
            for (int i = n - 1; i >= 0; i--) {
                revs[i] = (revs[i + 1] * (i + 1)) % m;
            }
        }

        public long combMod(int n, int k) {
            long ret = nors[n];
            ret = modulo.mlt(ret, revs[k]);
            ret = modulo.mlt(ret, revs[n - k]);
            return ret;
        }

    }
}