Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length n, a_1, ..., a_n.
Let us consider performing the following n operations on an empty sequence b.

The i-th operation is as follows:

Append a_i to the end of b.

Reverse the order of the elements in b.

Find the sequence b obtained after these n operations.

Constraints

1 \leq n \leq 2\times 10^5

0 \leq a_i \leq 10^9

n and a_i are integers.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print n integers in a line with spaces in between.
The i-th integer should be b_i.

Sample Input 1

4
1 2 3 4

Sample Output 1

4 2 1 3

After step 1 of the first operation, b becomes: 1.

After step 2 of the first operation, b becomes: 1.

After step 1 of the second operation, b becomes: 1, 2.

After step 2 of the second operation, b becomes: 2, 1.

After step 1 of the third operation, b becomes: 2, 1, 3.

After step 2 of the third operation, b becomes: 3, 1, 2.

After step 1 of the fourth operation, b becomes: 3, 1, 2, 4.

After step 2 of the fourth operation, b becomes: 4, 2, 1, 3.

Thus, the answer is 4 2 1 3.

Sample Input 2

3
1 2 3

Sample Output 2

3 1 2

As shown above in Sample Output 1, b becomes 3, 1, 2 after step 2 of the third operation. Thus, the answer is 3 1 2.

Sample Input 3

1
1000000000

Sample Output 3

1000000000

Sample Input 4

6
0 6 7 6 7 0

Sample Output 4

0 6 6 0 7 7

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	final long MODULO = 1_000_000_000 + 7;
	int n;
	int[] a;

	void run() {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		long[] fac = new long[n + 1];
		long[] revfac = new long[n + 1];
		long[] rev = new long[n + 1];
		fac[0] = 1;
		for (int i = 1; i < fac.length; ++i) {
			fac[i] = (fac[i - 1] * i) % MODULO;
		}
		rev[1] = 1;
		for (int i = 2; i < rev.length; ++i) {
			rev[i] = (MODULO - rev[(int) MODULO % i] * (MODULO / i) % MODULO) % MODULO;
		}
		revfac[0] = 1;
		for (int i = 1; i < revfac.length; ++i) {
			revfac[i] = (revfac[i - 1] * rev[i]) % MODULO;
		}

		a = new int[n + 1];
		int m = -1;
		boolean[] f = new boolean[n];
		for (int i = 0; i < n; ++i) {
			a[i] = sc.nextInt() - 1;
			if (f[a[i]]) {
				m = a[i];
			} else {
				f[a[i]] = true;
			}
		}
		int k1 = 0, k2 = 0, k3 = 0;
		int i;
		for (i = 0; i < n; ++i) {
			if (a[i] == m) {
				break;
			}
			++k1;
		}
		for (i = i + 1; i < n; ++i) {
			if (a[i] == m) {
				break;
			}
			++k2;
		}
		PrintWriter pw = new PrintWriter(System.out);
		k3 = n - 1 - (k1 + k2);
		for (int len = 1; len <= n + 1; ++len) {
			if (len == 1) {
				pw.println(n);
				continue;
			}
			long ans = 0;
			ans = comb(n - 1, len, fac, revfac);// m:0個
			ans = (ans + comb(n - 1, len - 2, fac, revfac)) % MODULO;// m:2個
			ans = (ans + 2 * comb(n - 1, len - 1, fac, revfac)) % MODULO;// m:1個
			ans = (ans - comb(k1 + k3, len - 1, fac, revfac) + MODULO) % MODULO;// m:1個
			pw.println(ans);
		}
		pw.close();

	}

	long comb(int n, int k, long[] fac, long[] revfac) {
		if (n < k)
			return 0;
		return fac[n] * revfac[k] % MODULO * revfac[n - k] % MODULO;
	}

	long pow(long a, long n) {
		long ret = 1;
		for (; n > 0; n >>= 1, a = (a * a) % MODULO) {
			if (n % 2 == 1)
				ret = (ret * a) % MODULO;
		}
		return ret;
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}