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 Rust (1.15.1) (judge verdict: Wrong Answer)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
fn modulo(i:usize,j:usize,p:usize) -> usize {
    let mut result = 1;
        let mut cur = i;
        let mut e = j;
        while e > 0 {
            if e & 1 == 1 {
                result *= cur;
                result%=p;
            }
            e >>= 1;
            cur *= cur;
            result%=p;
        }
        result
}

fn main() {
    input!{
        p: usize,
        a:[i64;p],
    }
    let mut b:Vec<i64> = vec![0;p];
    let mut fact:Vec<usize> = vec![0;p];
    let mut inv:Vec<usize> = vec![0;p];
    fact[0] = 1;
    fact[1] = 1;
    for i in 2..p {
        fact[i] = fact[i-1] * i % p;
    }
    inv[0] = 1;
    inv[1] = 1;
    for i in 2..p {
        inv[i] = (p - p/i) * inv[p%i] % p;
    }
    let mut fact_inv:Vec<usize> = vec![0;p];
    fact_inv[0]=1;
    fact_inv[1]=1;
    for i in 2..p {
        fact_inv[i] = fact_inv[i-1] * inv[i] % p;
    }

    for i in 0..p {
        if a[i] == 1 {
            b[0]+=1;
            for j in 0..p {
                b[j]-= ((fact[p-1] * fact_inv[p-1-j] % p * fact_inv[j] % p) * modulo(i, p-1-j, p)) as i64;
                b[j] *= if j%2==0 {1}else{-1};
                b[j]%=p as i64;
                if b[j] < 0 {
                    b[j]+=p as i64;
                }
            }
        }
    }
    for i in 0..p {
        if i==p-1 {
            println!("{}", b[i]);
        }else{
            print!("{} ", b[i]);
        }

    }
}