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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
using LL = long long;

#define fs first
#define sc second

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }


// std::vector Declaration
template<typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

// std::vector Initialization
template<typename T>
void fill_all(T& arr, const T& v) { arr = v; }
template<typename T, typename U>
void fill_all(T& arr, const U& v) { for (auto& i : arr) fill_all(i, v); }

// std::vector Debug
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "[";
    bool a = 1;
    for (auto e : v) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::deque Debug
template<typename T>
ostream& operator<<(ostream& os, const deque<T>& d) {
    os << "[";
    bool a = 1;
    for (auto e : d) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::pair Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << " " << p.second << ")";
    return os;
}

// std::set Debug
template<typename T>
ostream& operator<<(ostream& os, const set<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::multiset Debug
template<typename T>
ostream& operator<<(ostream& os, const multiset<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::map Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const map<T, U>& mp) {
    os << "{";
    bool a = 1;
    for (auto e : mp) {
        os << (a ? "" : " ");
        os << e.first << ":" << e.second;
        a = 0;
    }
    os << "}";
    return os;
}

// std::tuple Debug
template<int N, class Tuple>
void out(ostream& os, const Tuple& t){}
template<int N, class Tuple, class H, class ...Ts>
void out(ostream& os, const Tuple& t) {
    if (N) os << " ";
    os << get<N>(t);
    out<N+1,Tuple,Ts...>(os, t);
}
template<class ...Ts>
ostream& operator<<(ostream& os, const tuple<Ts...>& t) {
    os << "(";
    out<0,tuple<Ts...>,Ts...>(os, t);
    os << ")";
    return os;
}

// Debug
#define DUMP(x) cerr<<#x<<" = "<<(x)<<endl


struct edge { int to, cost; };
ostream& operator<<(ostream& os, const edge& e) {
    os << "(" << e.to << ", " << e.cost << ")";
    return os;
}

const LL LINF = 1LL<<60;
const int IINF = 1<<30;
const LL MOD = 1e9+7;

template<typename T>
class ModInt {
    static T& _getMod() {
        static T _mod = 0;
        return _mod;
    }

    public:
    static void setMod(const T m) { _getMod() = m; }
    static T mod() { return _getMod(); }

    T val;
    ModInt(T val=0) :
        val(((val % mod()) + mod()) % mod()) {}

    const ModInt operator+() const {
        return *this;
    }
    const ModInt operator-() const {
        return (-val + mod()) % mod();
    }
    const ModInt inverse() const {
        return pow(mod()-2);
    }

    ModInt& operator+=(const ModInt& rhs) {
        (val += rhs.val) %= mod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        return *this += -rhs;
    }
    ModInt& operator*=(const ModInt& rhs) {
        (val *= rhs.val) %= mod();
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) {
        return *this *= rhs.inverse();
    }

    const ModInt operator+(const ModInt& rhs) const {
        return ModInt(*this) += rhs;
    }
    const ModInt operator-(const ModInt& rhs) const {
        return ModInt(*this) -= rhs;
    }
    const ModInt operator*(const ModInt& rhs) const {
        return ModInt(*this) *= rhs;
    }
    const ModInt operator/(const ModInt& rhs) const {
        return ModInt(*this) /= rhs;
    }

    const ModInt pow(long long n) const {
        ModInt ret = 1, tmp = val;
        while (n > 0) {
            if (n & 1) ret *= tmp;
            tmp *= tmp;
            n >>= 1;
        }
        return ret;
    }

    bool operator==(const ModInt& rhs) const {
        return val == rhs.val;
    }
    bool operator!=(const ModInt& rhs) const {
        return !(*this == rhs);

    }

    friend const ModInt operator+(const T& lhs, const ModInt& rhs) {
        return ModInt(lhs) + rhs;
    }
    friend const ModInt operator-(const T& lhs, const ModInt& rhs) {
        return ModInt(lhs) - rhs;
    }
    friend const ModInt operator*(const T& lhs, const ModInt& rhs) {
        return ModInt(lhs) * rhs;
    }
    friend const ModInt operator/(const T& lhs, const ModInt& rhs) {
        return ModInt(lhs) / rhs;
    }

    friend bool operator==(const T& lhs, const ModInt& rhs) {
        return ModInt(lhs) == rhs;
    }
    friend bool operator!=(const T& lhs, const ModInt& rhs) {
        return ModInt(lhs) != rhs;
    }

    friend ostream& operator<<(ostream& os, const ModInt& a) {
        return os << a.val;
    }
    friend istream& operator>>(istream& is, ModInt& a) {
        T tmp; is >> tmp;
        a = tmp;
        return is;
    }
};

template<typename Field>
struct Polynomial {

    vector<Field> a;

    void reserve(int n) {
        if (a.size() < n) {
            a.resize(n);
        }
    }

    void trim() {
        //while (a.size() > 0 && a.back() == 0) {
        //    a.pop_back();
        //}
    }

    void shift(int n) {
        if (n > 0) {
            reserve(a.size() + n);
            for (int i = a.size()-1; i >= 0; --i) {
                a[i] = (i >= n ? a[i - n] : 0);
            }
        } else {
            n = -n;
            for (int i = 0; i < a.size(); ++i) {
                a[i] = (i < a.size()-n ? a[i + n] : 0);
            }
            trim();
        }
    }

    Polynomial() {}
    Polynomial(int n) { a.resize(n); }
    Polynomial(const vector<Field> init)
        : a(init.begin(), init.end()) {}
    Polynomial(const initializer_list<Field> init)
        : a(init.begin(), init.end()) {}

    const int size() const {
        return a.size();
    }

    const Field operator[](int i) const {
        return a[i];
    }

    const Field back() const {
        assert(a.size() > 0);
        return a[a.size()-1];
    }

    void set(int i, Field& val) {
        if (a.size() <= i) reserve(i+1);
        a[i] = val;
    }

    const Polynomial operator+() const {
        return *this;
    }
    const Polynomial operator-() const {
        vector<Field> ret(a);
        for (auto &e : ret) { e = -e; }
        return ret;
    }

    Polynomial& operator+=(const Polynomial& rhs) {
        reserve(rhs.size());
        for (int i = 0; i < rhs.size(); ++i) {
            a[i] += rhs[i];
        }
        trim();
        return *this;
    }
    Polynomial& operator-=(const Polynomial& rhs) {
        return *this += -rhs;
    }

    Polynomial& operator*=(const Field& rhs) {
        for (auto &e : a) { e *= rhs; }
        trim();
        return *this;
    }
    Polynomial& operator/=(const Field& rhs) {
        for (auto &e : a) { e /= rhs; }
        trim();
        return *this;
    }

    Polynomial& operator*=(const Polynomial& rhs) {
        Polynomial ret;

        for (int i = 0; i < rhs.size(); ++i) {
            ret += *this * rhs[i];
            shift(1);
        }

        ret.trim();
        return *this = ret;
    }

    Polynomial& operator/=(const Polynomial& rhs) {
        assert(rhs.size() != 0);

        Polynomial ret, tmp(rhs);

        ret.reserve(a.size() - rhs.size() + 1);
        tmp.shift(ret.size() - 1);

        for (int i = a.size() - 1; i >= rhs.size() - 1; --i) {
            Field q = a[i] / rhs.back();
            ret.set(i - rhs.size() + 1, q);
            *this -= tmp * q;
            tmp.shift(-1);
        }

        ret.trim();
        return *this = ret;
    }

    const Polynomial operator+(const Polynomial& rhs) const {
        return Polynomial(a) += rhs;
    }
    const Polynomial operator-(const Polynomial& rhs) const {
        return Polynomial(a) -= rhs;
    }
    const Polynomial operator*(const Field& rhs) const {
        return Polynomial(a) *= rhs;
    }
    const Polynomial operator/(const Field& rhs) const {
        return Polynomial(a) /= rhs;
    }
    const Polynomial operator*(const Polynomial& rhs) const {
        return Polynomial(a) *= rhs;
    }
    const Polynomial operator/(const Polynomial& rhs) const {
        return Polynomial(a) /= rhs;
    }

    const Polynomial pow(long long n) const {
        Polynomial ret({1}), tmp(a);
        while (n > 0) {
            if (n & 1) ret *= tmp;
            tmp *= Polynomial(tmp);
            n >>= 1;
        }

        ret.trim();
        return ret;
    }

    bool operator==(const Polynomial& rhs) const {
        if (a.size() != rhs.size()) {
            return false;
        }
        for (int i = 0; i < a.size(); ++i) {
            if (a[i] != rhs[i]) return false;
        }
        return true;
    }
    bool operator!=(const Polynomial& rhs) const {
        return !(*this == rhs);
    }

    friend ostream& operator<<(ostream& os, const Polynomial& p) {
        if (p.size() == 0) {
            return os << 0;
        }
        for (int i = p.size() - 1; i >= 0; --i) {
            if (p[i] == 0) {
                continue;
            }
            if (i != p.size() - 1) {
                os << " + ";
            }
            if (i == 0) {
                os << p[i];
            } else if (i == 1) {
                if (p[i] != 1) os << p[i];
                os << "x";
            } else {
                if (p[i] != 1) os << p[i];
                os << "x^" << i;
            }
        }
        return os;
    }
};

template<typename Ring>
struct Fact {
    vector<Ring> fact;
    Fact(int n) {
        fact.resize(n+1);
        fact[0] = Ring{1};
        for (int i = 1; i <= n; ++i) {
            fact[i] = fact[i-1] * i;
        }
    }
    Ring operator[](int i) {
        return fact[i];
    }
};

template<typename Field>
struct Comb {
    Fact<Field> fact;
    Comb(int n) : fact(n) {}
    Field operator()(int n, int r) {
        if (n < 0 || n-r < 0 || r < 0) {
            return 0;
        }
        return fact[n] / (fact[n-r] * fact[r]);
    }
};

int main()
{

    int p; cin >> p;

    using Int = ModInt<LL>;
    Int::setMod(p);
    using P = Polynomial<Int>;

    vector<Int> a(p);
    for (int i = 0; i < p; ++i) {
        cin >> a[i];
    }


    Comb<Int> comb(p-1);

    P ans(p);

    for (int i = 0; i < p; ++i) {
        P tmp(p);
        for (int j = 0; j < p; ++j) {
            Int b = comb(p-1, j) * Int(-i).pow(p-1-j);
            tmp.set(j, b);
        }
        ans += (P{1} - tmp) * a[i];
        //ans += (P{1} - P{-i, 1}.pow(p-1)) * a[i];
    }

    for (int i = 0; i < p; ++i) {
        cout << (i < ans.size() ? ans[i] : 0) << " ";
    }

    return 0;
}