結果

問題 No.2122 黄金比で擬似乱数生成
ユーザー haruki_K
提出日時 2022-11-04 22:50:41
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 17,612 bytes
コンパイル時間 1,942 ms
コンパイル使用メモリ 213,388 KB
最終ジャッジ日時 2025-02-08 18:13:39
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
other AC * 16 WA * 10
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// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
using pii = pair<int, int>;
#define rep(i, n) if (const int _rep_n = n; true) for (int i = 0; i < _rep_n; i++)
#define rep1(i, n) if (const int _rep_n = n; true) for (int i = 1; i <= _rep_n; i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#define oj_local(x, y) (y)
#else
#define dump(...) (void)(0)
#define debug if (0)
#define oj_local(x, y) (x)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear
    (); } };
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; }
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; }
template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t)
{ bool f = true; apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t); return os; }
template <class... T> istream& operator>>(istream& is, tuple<T...>& t) { apply([&](auto&&... x) { ((is >> x), ...); }, t); return is; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } };
#define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << '\n'; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); }
template <class T, class = decltype(begin(declval<T&>()))> constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); }
template <class T, class = decltype(begin(declval<T&>()))> constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); }
template <class T> constexpr T min(set<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(set<T> const& st) { assert(st.size()); return *prev(st.end()); }
template <class T> constexpr T min(multiset<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(multiset<T> const& st) { assert(st.size()); return *prev(st.end()); }
constexpr ll max(signed x, ll y) { return max<ll>(x, y); }
constexpr ll max(ll x, signed y) { return max<ll>(x, y); }
constexpr ll min(signed x, ll y) { return min<ll>(x, y); }
constexpr ll min(ll x, signed y) { return min<ll>(x, y); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }
template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }
constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
auto four_nbd(int n, int m) {
    static vector<pair<int, int>> v;
    return [n, m](int i, int j) {
        const int dx[] = { 1, 0, -1, 0 }, dy[] = { 0, 1, 0, -1 };
        v.clear();
        rep (dir, 4) {
            int ni = i+dx[dir], nj = j+dy[dir];
            if (0 <= ni and ni < n and 0 <= nj and nj < m) {
                v.emplace_back(ni, nj);
            }
        }
        return v;
    };
};
template <class Comp> vector<int> iota(int n, Comp comp) {
    vector<int> idx(n);
    iota(begin(idx), end(idx), 0);
    stable_sort(begin(idx), end(idx), comp);
    return idx;
}
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }
template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }
bool next_product(vector<int> &v, int m) {
    repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;
    return false;
}
bool next_product(vector<int> &v, vector<int> const& s) {
    repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;
    return false;
}
template <class vec> int sort_unique(vec &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class It> auto prefix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(s.back() + *l++);
    return s;
}
template <class It> auto suffix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(*--r + s.back());
    reverse(s.begin(), s.end());
    return s;
}
template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_back(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }
template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }
template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }
template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }
template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }
template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
// <<<
// >>> matrix
template <class T> struct semi_ring_one {
    template <class S>
    static decltype(S::one()) helper(signed) { return S::one(); }
    template <class S>
    static constexpr S helper(long) { return 1; }
    static T get() { return helper<T>(0); }
};
template <class T, int N, int M> struct MatrixBase {
    static_assert(N > 0 and M > 0);
    int n = N, m = M;
    array<T, N*M> a = {};
    MatrixBase() {}
    MatrixBase(int n, int m) { assert(N == n and M == m); }
};
template <class T> struct MatrixBase<T, -1, -1> {
    int n, m;
    vector<T> a;
    MatrixBase() : n(0), m(0) {}
    MatrixBase(int n, int m) : n(n), m(m), a(n*m) { assert(n > 0 and m > 0); }
};
template <class T, int N = -1, int M = -1> struct Matrix : MatrixBase<T, N, M> {
    using base = MatrixBase<T, N, M>;
    using base::base, base::n, base::m, base::a;
    Matrix(initializer_list<initializer_list<T>> init)
        : base(init.size(), init.begin()->size()) {
        int i = 0;
        for (auto const& ls : init) {
            assert((int)ls.size() == m);
            for (auto const& x : ls) {
                a[i++] = x;
            }
        }
    }
    auto operator[](int i) const {
        assert(0 <= i); assert(i < n);
        return a.begin() + i*m;
    }
    auto operator[](int i) {
        assert(0 <= i); assert(i < n);
        return a.begin() + i*m;
    }
    bool operator==(Matrix const& x) const {
        return n == x.n and m == x.m and a == x.a;
    }
    bool operator!=(Matrix const& x) const {
        return !(*this == x);
    }
    Matrix operator+() const { return *this; }
    Matrix operator+(Matrix const& x) const { return Matrix(*this) += x; }
    Matrix& operator+=(Matrix const& x) {
        assert(n == x.n and m == x.m);
        rep (i, a.size()) a[i] += x.a[i];
        return *this;
    }
    template <int L>
    Matrix<T, N, L> operator*(Matrix<T, M, L> const& x) const {
        assert(m == x.n);
        Matrix<T, N, L> ret(n, x.m);
        rep (i, n) rep (j, m) {
            auto A = ret[i];
            auto B = (*this)[i][j];
            auto C = x[j];
            rep (k, x.m) A[k] += B * C[k];
        }
        return ret;
    }
    Matrix& operator*=(Matrix const& x) {
        auto res = (*this)*x;
        swap(a, res.a);
        return *this;
    }
    Matrix operator*(T const& c) const { return Matrix(*this) *= c; }
    Matrix& operator*=(T const& c) {
        rep (i, a.size()) a[i] *= c;
        return *this;
    }
    friend Matrix operator*(T const& c, Matrix const& x) {
        Matrix ret = x;
        rep (i, ret.a.size()) ret.a[i] = c * ret.a[i];
        return ret;
    }
    static Matrix identity(int n = N) {
        static_assert(N == M);
        assert(n >= 0);
        Matrix ret(n, n);
        rep (i, n) ret[i][i] = semi_ring_one<T>::get();
        return ret;
    }
    Matrix pow(ll k) const {
        assert(n == m); assert(k >= 0);
        Matrix v = *this, r = identity(n);
        for ( ; k > 0; k >>= 1, v *= v) if (k & 1) r *= v;
        return r;
    }
    Matrix operator-() const {
        Matrix x = *this;
        rep (i, a.size()) a[i] = -a[i];
        return x;
    }
    Matrix& operator-=(Matrix const& x) {
        assert(n == x.n and m == x.m);
        rep (i, a.size()) a[i] -= x.a[i];
        return *this;
    }
    Matrix operator-(Matrix const& x) const { return Matrix(*this) -= x; }
    Matrix& operator/=(T const& c) {
        rep (i, a.size()) a[i] /= c;
        return *this;
    }
    Matrix operator/(T const& c) const {
        return Matrix(*this) /= c;
    }
    friend istream& operator>>(istream& is, Matrix& x) {
        rep (i, x.n) rep (j, x.m) is >> x[i][j];
        return is;
    }
#ifdef LOCAL
    friend string to_s(Matrix const& x) {
        string ret;
        rep (i, x.n) {
            ret += "\n(";
            rep (j, x.m) ret += " " + to_s(x[i][j]);
            ret += " )";
        }
        return ret += "\n";
    }
#endif
};
// <<<
// >>> runtime modint
template <int id> class runtime_modint {
    using u32 = uint32_t;
    using i32 = int32_t;
    using i64 = int64_t;
    using M = runtime_modint;
    u32 x;
    struct barrett_mul {
        uint32_t mod;
        uint64_t inv;
        barrett_mul() : mod(0), inv(0) { }
        barrett_mul(uint32_t mod) : mod(mod), inv((uint64_t)(-1) / mod + 1) { }
        uint32_t operator()(uint32_t a, uint32_t b) const {
            __uint128_t c = uint64_t(a) * b;
            uint64_t q = (c * inv) >> 64;
            uint32_t x = c - q * mod;
            if (mod <= x) x += mod;
            return x;
        }
    };
    inline static barrett_mul mul;
public:
    static void set_mod(u32 new_mod) { mul = barrett_mul(new_mod); }
    static int mod() { return mul.mod; }
    runtime_modint(i64 x = 0)
        : x((assert(mod() > 0), ((x %= (u32)mod()) < 0 ? x+mod() : x))) { }
    i64 val() const { return x; }
    constexpr explicit operator i64() const { return x; }
    bool operator==(M const& r) const { return x == r.x; }
    bool operator!=(M const& r) const { return x != r.x; }
    M operator+() const { return *this; }
    M operator-() const { return M()-*this; }
    M& operator+=(M const& r) { i64 t = i64(x) + r.x; if (t >= mod()) t -= mod(); x = t; return *this; }
    M& operator-=(M const& r) { i64 t = i64(x) + mod()-r.x; if (t >= mod()) t -= mod(); x = t; return *this; }
    M& operator*=(M const& r) { x = mul(x, r.x); return *this; }
    M& operator/=(M const& r) { return *this *= r.inv(); }
    M operator+(M r) const { return M(*this) += r; }
    M operator-(M r) const { return M(*this) -= r; }
    M operator*(M r) const { return M(*this) *= r; }
    M operator/(M r) const { return M(*this) /= r; }
    friend M operator+(i64 x, M y) { return M(x)+y; }
    friend M operator-(i64 x, M y) { return M(x)-y; }
    friend M operator*(i64 x, M y) { return M(x)*y; }
    friend M operator/(i64 x, M y) { return M(x)/y; }
    M pow(i64 n) const { // 0^0 = 1
        if (n < 0) return inv().pow(-n);
        M v = *this, r = 1;
        for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
        return r;
    }
    M inv() const {
        uint32_t a = x, b = mod();
        int64_t u = 1, v = 0;
        while (b) {
            int64_t q = a / b;
            swap(a -= q * b, b);
            swap(u -= q * v, v);
        }
        assert(a == 1);
        return u;
    }
    static i64 gen() { // assume mod():prime
        if (mod() == 2) return 1;
        assert(mod() >= 3);
        for (int i = 2; i*i <= mod(); i++) assert(mod() % i != 0);
        vector<int> ps;
        int n = mod()-1;
        for (int i = 2; i*i <= n; ++i) {
            if (n % i) continue;
            ps.push_back(i);
            do n /= i; while (n % i == 0);
        }
        if (n > 1) ps.push_back(n);
        n = mod()-1;
        auto check = [&](M g) {
            for (int p : ps) if (g.pow(n/p) == 1) return false;
            return true;
        };
        for (int g = 2; g <= n; ++g) if (check(g)) return g;
        return -1;
    }
    // return minimum k >= (allow_zero ? 0 : 1) s.t. this->pow(k) == y
    // return -1 if not found
    int log(M y, bool allow_zero = false) {
        if (allow_zero and pow(0) == y) return 0;
        auto x = *this;
        M z = 1;
        int k = 0;
        while ((1u << k) < mod()) {
            z *= x, k++;
            if (z == y) return k;
        }
        u32 g = gcd(z.x, mod());
        if (y.x % g != 0) return -1;
        auto old_mul = mul;
        mul = barrett_mul(mod()/g);
        x.x %= mod(), y.x /= g, z.x /= g;
        unordered_map<u32, u32> m;
        int s = 0;
        M w = 1;
        for ( ; s*s < mod(); s++) m[(y*w).x] = s, w *= x;
        while (k < mod()) {
            z *= w, k += s;
            if (m.count(z.x)) {
                swap(mul, old_mul);
                return k - m[z.x];
            }
        }
        swap(mul, old_mul);
        return -1;
    }
#ifdef LOCAL
//    friend string to_s(M r) { return to_s(r.val(), M::mod()); }
    friend string to_s(M r) { return to_s(r.val()); }
#endif
    friend ostream& operator<<(ostream& os, M r) { return os << r.val(); }
    friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }
};
using mint = runtime_modint<-1>;
// <<<
int32_t main() {
    const int N = 10000;
    mint::set_mod(N);
    int s, m, L; cin >> s >> m >> L;
    dump(s);
    auto f = [&](int n) -> int {
        if (m == 0) {
            return 0;
        } else {
            Matrix<mint> A = {
                { n, 1 },
                { 1, 0 }
            };
            A = A.pow(m-1);
            return A[0][0].val();
        }
    };
    const int LG = 62;
    auto to = make_v<int, 2>(LG, N);
    rep (i, N) to[0][i] = f(i);
    rep (k, LG-1) rep (i, N) to[k+1][i] = to[k][to[k][i]];
    debug {
        auto to_ = to[0];
        to_.resize(10);
        dump(to_);
    }
    rep (k, LG) if (L>>k&1) {
        s = to[k][s];
    }
    cout << setfill('0') << setw(4) << s << '\n';
}
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