Problem:
Score : 600 points

Problem Statement

Given are a prime number p and a sequence of p integers a_0, \ldots, a_{p-1} consisting of zeros and ones.

Find a polynomial of degree at most p-1, f(x) = b_{p-1} x^{p-1} + b_{p-2} x^{p-2} + \ldots + b_0, satisfying the following conditions:

For each i (0 \leq i \leq p-1), b_i is an integer such that 0 \leq b_i \leq p-1.

For each i (0 \leq i \leq p-1), f(i) \equiv a_i \pmod p.

Constraints

2 \leq p \leq 2999

p is a prime number.

0 \leq a_i \leq 1

Input

Input is given from Standard Input in the following format:

p
a_0 a_1 \ldots a_{p-1}

Output

Print b_0, b_1, \ldots, b_{p-1} of a polynomial f(x) satisfying the conditions, in this order, with spaces in between.

It can be proved that a solution always exists. If multiple solutions exist, any of them will be accepted.

Sample Input 1

2
1 0

Sample Output 1

1 1

f(x) = x + 1 satisfies the conditions, as follows:

f(0) = 0 + 1 = 1 \equiv 1 \pmod 2

f(1) = 1 + 1 = 2 \equiv 0 \pmod 2

Sample Input 2

3
0 0 0

Sample Output 2

0 0 0

f(x) = 0 is also valid.

Sample Input 3

5
0 1 0 1 0

Sample Output 3

0 2 0 1 3

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

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

public class Main {
    public static final Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
    public static final PrintStream out = System.out;

    public static void main(String[] args) {
        int P = in.nextInt();
        int[] A = new int[P];
        int[] B = new int[P];

        for (int i = 0; i < P; i++) {
            A[i] = in.nextInt();
        }

        B[0] = A[0];
        
        for (int i = 1; i < P; i++) {
            B[P - 1] = (B[P - 1] + A[i] - B[0] + P) % P;
        }
        B[P - 1] = (P - B[P - 1]) % P;

        for (int i = P - 2; 0 < i; i--) {
            for (int j = 1; j < P; j++) {
                A[j] = (A[j] * j) % P;
                B[i] = (B[i] + A[j]) % P;
            }
            B[i] = (P - B[i]) % P;
        }
        
        out.println(Arrays.toString(B));
    }
}