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.util.Arrays;
import java.util.function.ToLongBiFunction;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {

	public static void main(String args[]) {
		FastScanner cin = new FastScanner(System.in);
		PrintWriter cout = new PrintWriter(System.out);
		solve(cin, cout);
		cout.flush();
	}

	private static void solve(FastScanner cin, PrintWriter cout) {
		assert Arrays.equals(solve(3, new int[] { 1, 2, 1, 3 }), new long[] { 3, 5, 4, 1 });
		assert Arrays.equals(solve(1, new int[] { 1, 1 }), new long[] { 1, 1 });
		assert Arrays.equals(
				solve(32,
						new int[] { 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 }),
				new long[] { 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 });

		int n = cin.nextInt();
		int[] a = new int[n + 1];
		for (int i = 0; i < a.length; i++)
			a[i] = cin.nextInt();

		long[] ans = solve(n, a);
		String ansstr = Arrays.stream(ans).mapToObj(Long::toString).collect(Collectors.joining(System.lineSeparator()));
		cout.println(ansstr);
	}

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

	private static long[] solve(int n, int[] a) {
		int dupval = -1;
		int duppos = -1;
		Integer[] pos = new Integer[n + 1];
		for (int i = 0; i < a.length; i++) {
			if (pos[a[i]] == null) {
				pos[a[i]] = i;
				continue;
			}
			dupval = a[i];
			duppos = i;
		}

		// 組み合わせ(mod x)を計算
		int combsize = n + 2;
		ToLongBiFunction<Integer, Integer> combination = new ToLongBiFunction<Integer, Integer>() {
			private final long[] modfact;
			private final long[] modinv;
			{
				modfact = new long[combsize];
				modfact[0] = 1;
				for (int i = 1; i < combsize; i++)
					modfact[i] = (modfact[i - 1] * i) % MOD;

				modinv = new long[combsize];
				Arrays.fill(modinv, 1);
				for (int i = combsize - 1; i >= 0; i--)
					// BigInteger.valueOf(modfact[i]).modInverse(BigInteger.valueOf(MOD)).longValueExact();
					for (long p = modfact[i], e = MOD - 2; e != 0; e >>= 1, p = (p * p) % MOD)
						if ((e & 1) == 1)
							modinv[i] = (modinv[i] * p) % MOD;
			}

			@Override
			public long applyAsLong(Integer n, Integer k) {
				if (0 > k || k > n)
					return 0;
				// モンゴメリ乗算
				// https://en.wikipedia.org/wiki/Montgomery_modular_multiplication
				long ans = modfact[n];
				ans *= modinv[n - k];
				ans %= MOD;
				ans *= modinv[k];
				ans %= MOD;
				return ans;
			}

		};

		int outer = n - duppos + pos[dupval];
		long[] ans = IntStream.rangeClosed(1, n + 1).mapToLong((r) -> {
			long t = combination.applyAsLong(n + 1, r);
			t -= combination.applyAsLong(outer, r - 1);
			t += MOD;
			t %= MOD;
			return t;
		}).toArray();
		return ans;
	}

	static class FastScanner {
		private final InputStream in;
		private final byte[] buf = new byte[1 << 14];
		private int bufs = 0;
		private final long[] num = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
		private int ptr = 0;

		public FastScanner(InputStream in) {
			super();
			this.in = in;
		}

		boolean hasNext() {
			while (hasNextByte() && !isMeaningful(buf[ptr]))
				ptr++;
			return hasNextByte();
		}

		private boolean hasNextByte() {
			if (ptr < bufs)
				return true;
			ptr = 0;
			try {
				bufs = in.read(buf);
			} catch (IOException e) {
				throw new IllegalArgumentException(e);
			}
			if (bufs <= 0)
				return false;
			return true;
		}

		private static boolean isMeaningful(int b) {
			return 33 <= b && b <= 126;
			// return b != -1 && !Character.isWhitespace(b);
		}

		String next() {
			if (!hasNext())
				throw new IllegalArgumentException();
			StringBuilder sb = new StringBuilder();
			int b = read();
			while (isMeaningful(b)) {
				sb.appendCodePoint(b);
				b = read();
			}
			return sb.toString();
		}

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

		int nextInt() {
			long nl = nextLong();
			int ni = (int) nl;
			if (ni != nl)
				throw new IllegalArgumentException();
			return ni;
		}

		long nextLong() {
			if (!hasNext())
				throw new IllegalArgumentException();
			long n = 0;
			int plus = 1;
			int b = read();
			if (b == '-') {
				plus = -1;
				b = read();
			}
			if ('0' > b || b > '9')
				throw new java.lang.IllegalArgumentException();
			while (true) {
				if (!isMeaningful(b))
					return plus * n;
				n *= 10;
				n += num[b - '0'];
				b = read();
			}
		}

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

	}
}
