#814184 (C++23) No.2122 黄金比で擬似乱数生成

• 問題: No.2122 黄金比で擬似乱数生成
• ユーザー: hitonanode
• 提出日時: 2022-11-04 22:13:13
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: RE
• 実行時間: -
• コード長: 23,902 bytes
• コンパイル時間: 2,173 ms
• コンパイル使用メモリ: 192,668 KB
• 実行使用メモリ: 13,896 KB
• 最終ジャッジ日時: 2024-07-18 20:02:44
• 合計ジャッジ時間: 5,865 ms
• ジャッジサーバーID （参考情報）: judge4 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	RE	-
testcase_12	TLE	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-

ソースコード

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif


struct ModIntRuntime {
private:
    static int md;

public:
    using lint = long long;
    static int mod() { return md; }
    int val_;
    static std::vector<ModIntRuntime> &facs() {
        static std::vector<ModIntRuntime> facs_;
        return facs_;
    }
    static int &get_primitive_root() {
        static int primitive_root_ = 0;
        if (!primitive_root_) {
            primitive_root_ = [&]() {
                std::set<int> fac;
                int v = md - 1;
                for (lint i = 2; i * i <= v; i++)
                    while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < md; g++) {
                    bool ok = true;
                    for (auto i : fac)
                        if (ModIntRuntime(g).power((md - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root_;
    }
    static void set_mod(const int &m) {
        if (md != m) facs().clear();
        md = m;
        get_primitive_root() = 0;
    }
    ModIntRuntime &_setval(lint v) {
        val_ = (v >= md ? v - md : v);
        return *this;
    }
    int val() const noexcept { return val_; }
    ModIntRuntime() : val_(0) {}
    ModIntRuntime(lint v) { _setval(v % md + md); }
    explicit operator bool() const { return val_ != 0; }
    ModIntRuntime operator+(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ + x.val_);
    }
    ModIntRuntime operator-(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ - x.val_ + md);
    }
    ModIntRuntime operator*(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ * x.val_ % md);
    }
    ModIntRuntime operator/(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ * x.inv().val() % md);
    }
    ModIntRuntime operator-() const { return ModIntRuntime()._setval(md - val_); }
    ModIntRuntime &operator+=(const ModIntRuntime &x) { return *this = *this + x; }
    ModIntRuntime &operator-=(const ModIntRuntime &x) { return *this = *this - x; }
    ModIntRuntime &operator*=(const ModIntRuntime &x) { return *this = *this * x; }
    ModIntRuntime &operator/=(const ModIntRuntime &x) { return *this = *this / x; }
    friend ModIntRuntime operator+(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md + x.val_);
    }
    friend ModIntRuntime operator-(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md - x.val_ + md);
    }
    friend ModIntRuntime operator*(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md * x.val_ % md);
    }
    friend ModIntRuntime operator/(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md * x.inv().val() % md);
    }
    bool operator==(const ModIntRuntime &x) const { return val_ == x.val_; }
    bool operator!=(const ModIntRuntime &x) const { return val_ != x.val_; }
    bool operator<(const ModIntRuntime &x) const {
        return val_ < x.val_;
    } // To use std::map<ModIntRuntime, T>
    friend std::istream &operator>>(std::istream &is, ModIntRuntime &x) {
        lint t;
        return is >> t, x = ModIntRuntime(t), is;
    }
    friend std::ostream &operator<<(std::ostream &os, const ModIntRuntime &x) {
        return os << x.val_;
    }

    lint power(lint n) const {
        lint ans = 1, tmp = this->val_;
        while (n) {
            if (n & 1) ans = ans * tmp % md;
            tmp = tmp * tmp % md;
            n /= 2;
        }
        return ans;
    }
    ModIntRuntime pow(lint n) const { return power(n); }
    ModIntRuntime inv() const { return this->pow(md - 2); }

    ModIntRuntime fac() const {
        int l0 = facs().size();
        if (l0 > this->val_) return facs()[this->val_];

        facs().resize(this->val_ + 1);
        for (int i = l0; i <= this->val_; i++)
            facs()[i] = (i == 0 ? ModIntRuntime(1) : facs()[i - 1] * ModIntRuntime(i));
        return facs()[this->val_];
    }

    ModIntRuntime doublefac() const {
        lint k = (this->val_ + 1) / 2;
        return (this->val_ & 1)
                   ? ModIntRuntime(k * 2).fac() / (ModIntRuntime(2).pow(k) * ModIntRuntime(k).fac())
                   : ModIntRuntime(k).fac() * ModIntRuntime(2).pow(k);
    }

    ModIntRuntime nCr(const ModIntRuntime &r) const {
        return (this->val_ < r.val_) ? ModIntRuntime(0)
                                     : this->fac() / ((*this - r).fac() * r.fac());
    }

    ModIntRuntime sqrt() const {
        if (val_ == 0) return 0;
        if (md == 2) return val_;
        if (power((md - 1) / 2) != 1) return 0;
        ModIntRuntime b = 1;
        while (b.power((md - 1) / 2) == 1) b += 1;
        int e = 0, m = md - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModIntRuntime x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModIntRuntime z = b.power(m);
        while (y != 1) {
            int j = 0;
            ModIntRuntime t = y;
            while (t != 1) j++, t *= t;
            z = z.power(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModIntRuntime(std::min(x.val_, md - x.val_));
    }
};
int ModIntRuntime::md = 1;
using mint = ModIntRuntime;

namespace matrix_ {
struct has_id_method_impl {
    template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type());
    template <class T_> static auto check(...) -> std::false_type;
};
template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {};
} // namespace matrix_

template <typename T> struct matrix {
    int H, W;
    std::vector<T> elem;
    typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }
    inline T &at(int i, int j) { return elem[i * W + j]; }
    inline T get(int i, int j) const { return elem[i * W + j]; }
    int height() const { return H; }
    int width() const { return W; }
    std::vector<std::vector<T>> vecvec() const {
        std::vector<std::vector<T>> ret(H);
        for (int i = 0; i < H; i++) {
            std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));
        }
        return ret;
    }
    operator std::vector<std::vector<T>>() const { return vecvec(); }
    matrix() = default;
    matrix(int H, int W) : H(H), W(W), elem(H * W) {}
    matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {
        for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));
    }

    template <typename T2, typename std::enable_if<matrix_::has_id<T2>::value>::type * = nullptr>
    static T2 _T_id() {
        return T2::id();
    }
    template <typename T2, typename std::enable_if<!matrix_::has_id<T2>::value>::type * = nullptr>
    static T2 _T_id() {
        return T2(1);
    }

    static matrix Identity(int N) {
        matrix ret(N, N);
        for (int i = 0; i < N; i++) ret.at(i, i) = _T_id<T>();
        return ret;
    }

    matrix operator-() const {
        matrix ret(H, W);
        for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];
        return ret;
    }
    matrix operator*(const T &v) const {
        matrix ret = *this;
        for (auto &x : ret.elem) x *= v;
        return ret;
    }
    matrix operator/(const T &v) const {
        matrix ret = *this;
        const T vinv = _T_id<T>() / v;
        for (auto &x : ret.elem) x *= vinv;
        return ret;
    }
    matrix operator+(const matrix &r) const {
        matrix ret = *this;
        for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];
        return ret;
    }
    matrix operator-(const matrix &r) const {
        matrix ret = *this;
        for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];
        return ret;
    }
    matrix operator*(const matrix &r) const {
        matrix ret(H, r.W);
        for (int i = 0; i < H; i++) {
            for (int k = 0; k < W; k++) {
                for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);
            }
        }
        return ret;
    }
    matrix &operator*=(const T &v) { return *this = *this * v; }
    matrix &operator/=(const T &v) { return *this = *this / v; }
    matrix &operator+=(const matrix &r) { return *this = *this + r; }
    matrix &operator-=(const matrix &r) { return *this = *this - r; }
    matrix &operator*=(const matrix &r) { return *this = *this * r; }
    bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }
    bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }
    bool operator<(const matrix &r) const { return elem < r.elem; }
    matrix pow(int64_t n) const {
        matrix ret = Identity(H);
        bool ret_is_id = true;
        if (n == 0) return ret;
        for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
            if (!ret_is_id) ret *= ret;
            if ((n >> i) & 1) ret *= (*this), ret_is_id = false;
        }
        return ret;
    }
    std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {
        matrix x = *this;
        while (n) {
            if (n & 1) vec = x * vec;
            x *= x;
            n >>= 1;
        }
        return vec;
    };
    matrix transpose() const {
        matrix ret(W, H);
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);
        }
        return ret;
    }
    // Gauss-Jordan elimination
    // - Require inverse for every non-zero element
    // - Complexity: O(H^2 W)
    template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>
    static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
        int piv = -1;
        for (int j = h; j < mtr.H; j++) {
            if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c))))
                piv = j;
        }
        return piv;
    }
    template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>
    static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
        for (int j = h; j < mtr.H; j++) {
            if (mtr.get(j, c) != T2()) return j;
        }
        return -1;
    }
    matrix gauss_jordan() const {
        int c = 0;
        matrix mtr(*this);
        std::vector<int> ws;
        ws.reserve(W);
        for (int h = 0; h < H; h++) {
            if (c == W) break;
            int piv = choose_pivot(mtr, h, c);
            if (piv == -1) {
                c++;
                h--;
                continue;
            }
            if (h != piv) {
                for (int w = 0; w < W; w++) {
                    std::swap(mtr[piv][w], mtr[h][w]);
                    mtr.at(piv, w) *= -_T_id<T>(); // To preserve sign of determinant
                }
            }
            ws.clear();
            for (int w = c; w < W; w++) {
                if (mtr.at(h, w) != T()) ws.emplace_back(w);
            }
            const T hcinv = _T_id<T>() / mtr.at(h, c);
            for (int hh = 0; hh < H; hh++)
                if (hh != h) {
                    const T coeff = mtr.at(hh, c) * hcinv;
                    for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;
                    mtr.at(hh, c) = T();
                }
            c++;
        }
        return mtr;
    }
    int rank_of_gauss_jordan() const {
        for (int i = H * W - 1; i >= 0; i--) {
            if (elem[i] != 0) return i / W + 1;
        }
        return 0;
    }
    int rank() const { return gauss_jordan().rank_of_gauss_jordan(); }

    T determinant_of_upper_triangle() const {
        T ret = _T_id<T>();
        for (int i = 0; i < H; i++) ret *= get(i, i);
        return ret;
    }
    int inverse() {
        assert(H == W);
        std::vector<std::vector<T>> ret = Identity(H), tmp = *this;
        int rank = 0;
        for (int i = 0; i < H; i++) {
            int ti = i;
            while (ti < H and tmp[ti][i] == 0) ti++;
            if (ti == H) {
                continue;
            } else {
                rank++;
            }
            ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);
            T inv = _T_id<T>() / tmp[i][i];
            for (int j = 0; j < W; j++) ret[i][j] *= inv;
            for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;
            for (int h = 0; h < H; h++) {
                if (i == h) continue;
                const T c = -tmp[h][i];
                for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;
                for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;
            }
        }
        *this = ret;
        return rank;
    }
    friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {
        assert(m.W == int(v.size()));
        std::vector<T> ret(m.H);
        for (int i = 0; i < m.H; i++) {
            for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];
        }
        return ret;
    }
    friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {
        assert(int(v.size()) == m.H);
        std::vector<T> ret(m.W);
        for (int i = 0; i < m.H; i++) {
            for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);
        }
        return ret;
    }
    std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }
    std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }
    template <class OStream> friend OStream &operator<<(OStream &os, const matrix &x) {
        os << "[(" << x.H << " * " << x.W << " matrix)";
        os << "\n[column sums: ";
        for (int j = 0; j < x.W; j++) {
            T s = 0;
            for (int i = 0; i < x.H; i++) s += x.get(i, j);
            os << s << ",";
        }
        os << "]";
        for (int i = 0; i < x.H; i++) {
            os << "\n[";
            for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";
            os << "]";
        }
        os << "]\n";
        return os;
    }
    template <class IStream> friend IStream &operator>>(IStream &is, matrix &x) {
        for (auto &v : x.elem) is >> v;
        return is;
    }
};


// Solve ax^2 + bx + c = 0.
// retval: (# of solutions (-1 == inf.), solutions(ascending order))
// Verify: <https://yukicoder.me/problems/no/955> <https://atcoder.jp/contests/tricky/tasks/tricky_2>
template <typename Float>
std::pair<int, std::vector<Float>> quadratic_solver(Float A, Float B, Float C) {
    if (B < 0) A = -A, B = -B, C = -C;
    if (A == 0) {
        if (B == 0) {
            if (C == 0)
                return std::make_pair(-1, std::vector<Float>{}); // all real numbers
            else
                return std::make_pair(0, std::vector<Float>{}); // no solution
        } else
            return std::make_pair(1, std::vector<Float>{-C / B});
    }
    Float D = B * B - 4 * A * C;
    if (D < 0) return std::make_pair(0, std::vector<Float>{});
    if (D == 0) return std::make_pair(1, std::vector<Float>{-B / (2 * A)});
    Float ret1 = (-B - sqrt(D)) / (2 * A), ret2 = C / A / ret1;
    if (ret1 > ret2) std::swap(ret1, ret2);
    return std::make_pair(2, std::vector<Float>{ret1, ret2});
}

int run(int n, lint m) {
    int D = n * n + 4;

    // alpha^m / sqrtd の小数部分は beta^m / sqrtd の小数部分と等しい
    // double beta = quadratic_solver<double>(1, -n, -1).first;
    // auto ret = pow(beta, m) / sqrt(D);
    // if (ret < 0) ret += 1;
    // return floorl(ret * 10000);

    vector<mint> init{0, 1};
    matrix<mint> mat(2, 2);
    mat[0][1] = 1;
    mat[1][0] = 1;
    mat[1][1] = n;

    auto ret = mat.pow_vec(m, init).front();
    if (m % 2 == 1) ret -= 1;
    return ret.val();
}

void jikken(int n) {
    double d = n * n + 4;
    double sqrtd = sqrt(d);
    double p = (n + sqrtd) / 2;
    double q = (n - sqrtd) / 2;
    dbg(d);
    dbg(make_pair(p, q));
    dbg((p - q) / sqrtd);
    dbg((p * p - q * q) / sqrtd);
    dbg((p * p * p - q * q * q) / sqrtd);
    dbg((p * p * p * p - q * q * q * q) / sqrtd);
    dbg((p * p * p * p * p - q * q * q * q * q) / sqrtd);
}

int main() {
    mint::set_mod(10000);
    jikken(2);
    jikken(3);
    jikken(4);
    jikken(5);
    jikken(6);
    int N;
    lint M, L;
    cin >> N >> M >> L;
    dbg(make_tuple(N, M, L));

    map<int, lint> memo;
    memo[N] = 0;

    for (lint t = 0; t < L; ++t) {
        N = run(N, M);
        if (memo.count(N)) {
            lint rec = memo.count(N) - t;
            lint sk = floor_div(L - t, rec);
            if (sk > 1) { t += (sk - 1) * rec; }
        }
        memo[N] = t + 1;
    }
    string ret = to_string(N);
    while (ret.size() < 4) ret = "0" + ret;
    cout << ret << endl;
}