結果

問題 No.997 Jumping Kangaroo
ユーザー PachicobuePachicobue
提出日時 2020-02-21 22:57:46
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 18,554 bytes
コンパイル時間 2,579 ms
コンパイル使用メモリ 212,148 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-08 22:35:31
合計ジャッジ時間 3,802 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
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
5,248 KB
testcase_02 AC 87 ms
5,248 KB
testcase_03 WA -
testcase_04 WA -
testcase_05 WA -
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
testcase_10 AC 2 ms
5,248 KB
testcase_11 WA -
testcase_12 WA -
testcase_13 AC 11 ms
5,248 KB
testcase_14 WA -
testcase_15 WA -
testcase_16 WA -
testcase_17 AC 3 ms
5,248 KB
testcase_18 WA -
testcase_19 WA -
testcase_20 WA -
testcase_21 WA -
testcase_22 WA -
testcase_23 WA -
testcase_24 WA -
testcase_25 WA -
testcase_26 AC 2 ms
5,248 KB
testcase_27 AC 2 ms
5,248 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
// created [2020/02/21] 21:21:37
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"

using i32   = int32_t;
using i64   = int64_t;
using u32   = uint32_t;
using u64   = uint64_t;
using uint  = unsigned int;
using usize = std::size_t;
using ll    = long long;
using ull   = unsigned long long;
using ld    = long double;
template<typename T, usize n>
using arr = T (&)[n];
template<typename T, usize n>
using c_arr = const T (&)[n];
template<typename T>
using max_heap = std::priority_queue<T>;
template<typename T>
using min_heap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }
template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }
template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }
template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }
template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }
template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }
template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }
template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }
template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }
template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }
template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >> (64 - ind)); }
template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
constexpr unsigned int mod                  = 1000000007;
template<typename T> constexpr T inf_v      = std::numeric_limits<T>::max() / 4;
template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};
auto mfp = [](auto&& f) { return [=](auto&&... args) { return f(f, std::forward<decltype(args)>(args)...); }; };

template<typename T>
T in()
{
    T v;
    return std::cin >> v, v;
}
template<typename T, typename Uint, usize n, usize i>
T in_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type) { return in<T>(); }
template<typename T, typename Uint, usize n, usize i>
auto in_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type& szs)
{
    const usize s = (usize)szs[i];
    std::vector<decltype(in_v<T, Uint, n, i + 1>(szs))> ans(s);
    for (usize j = 0; j < s; j++) { ans[j] = in_v<T, Uint, n, i + 1>(szs); }
    return ans;
}
template<typename T, typename Uint, usize n>
auto in_v(c_arr<Uint, n> szs) { return in_v<T, Uint, n, 0>(szs); }
template<typename... Types>
auto in_t() { return std::tuple<std::decay_t<Types>...>{in<Types>()...}; }
struct io_init
{
    io_init()
    {
        std::cin.tie(nullptr), std::ios::sync_with_stdio(false);
        std::cout << std::fixed << std::setprecision(20);
    }
    void clear()
    {
        std::cin.tie(), std::ios::sync_with_stdio(true);
    }
} io_setting;

int out() { return 0; }
template<typename T>
int out(const T& v) { return std::cout << v, 0; }
template<typename T>
int out(const std::vector<T>& v)
{
    for (usize i = 0; i < v.size(); i++) {
        if (i > 0) { std::cout << ' '; }
        out(v[i]);
    }
    return 0;
}
template<typename T1, typename T2>
int out(const std::pair<T1, T2>& v) { return out(v.first), std::cout << ' ', out(v.second), 0; }
template<typename T, typename... Args>
int out(const T& v, const Args... args) { return out(v), std::cout << ' ', out(args...), 0; }
template<typename... Args>
int outln(const Args... args) { return out(args...), std::cout << '\n', 0; }
template<typename... Args>
int outel(const Args... args) { return out(args...), std::cout << std::endl, 0; }
#    define SHOW(...) static_cast<void>(0)
constexpr ull TEN(const usize n) { return n == 0 ? 1ULL : TEN(n - 1) * 10ULL; }

template<typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i == n), c_arr<Uint, n>>::type, const T& v = T{}) { return v; }
template<typename T, typename Uint, usize n, usize i>
auto make_v(typename std::enable_if<(i < n), c_arr<Uint, n>>::type szs, const T& v = T{})
{
    const usize s = (usize)szs[i];
    return std::vector<decltype(make_v<T, Uint, n, i + 1>(szs, v))>(s, make_v<T, Uint, n, i + 1>(szs, v));
}
template<typename T, typename Uint, usize n>
auto make_v(c_arr<Uint, n> szs, const T& t = T{}) { return make_v<T, Uint, n, 0>(szs, t); }

template<typename Ring>
class matrix
{
public:
    using value_type = Ring;
    matrix(const usize row, const usize column) : row{row}, column{column}, table(row, std::vector<value_type>(column, 0)) {}
    matrix(const matrix& m) : row{m.row}, column{m.column}, table{m.table} {}
    matrix& operator=(const matrix& m)
    {
        assert(row == m.row), assert(column == m.column);
        for (usize i = 0; i < row; i++) {
            for (usize j = 0; j < column; j++) { table[i][j] = m[i][j]; }
        }
        return *this;
    }
    const std::vector<value_type>& operator[](const usize r) const { return assert(r < row), table[r]; }
    std::vector<value_type>& operator[](const usize r) { return assert(r < row), table[r]; }
    friend matrix operator+(const matrix& m) { return m; }
    friend matrix operator-(const matrix& m)
    {
        matrix ans(m.row, m.column);
        for (usize r = 0; r < m.row; r++) {
            for (usize c = 0; c < m.column; c++) { ans.table[r][c] = -m.table[r][c]; }
        }
        return ans;
    }
    friend matrix operator+(const matrix& m1, const matrix& m2)
    {
        assert(m1.row == m2.row), assert(m1.column == m2.column);
        matrix ans(m1.row, m1.column);
        for (usize i = 0; i < m1.row; i++) {
            for (usize j = 0; j < m1.column; j++) { ans[i][j] = m1.table[i][j] + m2.table[i][j]; }
        }
        return ans;
    }
    friend matrix operator-(const matrix& m1, const matrix& m2)
    {
        assert(m1.row == m2.row), assert(m1.column == m2.column);
        matrix ans(m1.row, m1.column);
        for (usize i = 0; i < m1.row; i++) {
            for (usize j = 0; j < m1.column; j++) { ans[i][j] = m1.table[i][j] - m2.table[i][j]; }
        }
        return ans;
    }
    friend matrix operator*(const matrix& m1, const matrix& m2)
    {
        assert(m1.column == m2.row);
        matrix ans(m1.row, m2.column);
        for (usize i = 0; i < m1.row; i++) {
            for (usize j = 0; j < m2.column; j++) {
                for (usize k = 0; k < m1.column; k++) { ans[i][j] += m1.table[i][k] * m2.table[k][j]; }
            }
        }
        return ans;
    }
    friend matrix operator*(const matrix& m, const value_type& t)
    {
        matrix ans(m.row, m.column);
        for (usize i = 0; i < m.row; i++) {
            for (usize j = 0; j < m.column; j++) { ans[i][j] = m.table[i][j] * t; }
        }
        return ans;
    }
    friend matrix operator/(const matrix& m, const value_type& t)
    {
        assert(t != static_cast<value_type>(0));
        matrix ans(m.row, m.column);
        for (usize i = 0; i < m.row; i++) {
            for (usize j = 0; j < m.column; j++) { ans[i][j] = m.table[i][j] / t; }
        }
        return ans;
    }
    friend matrix operator*(const value_type& t, const matrix& m) { return m * t; }
    friend matrix operator^(const matrix& m, const unsigned long long n) { return assert(m.row == m.column), n == 0 ? matrix::id(m.row) : n % 2 == 1 ? m*(m ^ (n - 1)) : ((m * m) ^ (n / 2)); }
    friend matrix& operator+=(matrix& m1, const matrix& m2)
    {
        assert(m1.row == m2.row), assert(m1.column == m2.column);
        for (usize i = 0; i < m1.row; i++) {
            for (usize j = 0; j < m1.column; j++) { m1.table[i][j] += m2.table[i][j]; }
        }
        return m1;
    }
    friend matrix& operator-=(matrix& m1, const matrix& m2)
    {
        assert(m1.row == m2.row), assert(m1.column == m2.column);
        for (usize i = 0; i < m1.row; i++) {
            for (usize j = 0; j < m1.column; j++) { m1.table[i][j] -= m2.table[i][j]; }
        }
        return m1;
    }
    friend matrix& operator*=(matrix& m1, const matrix& m2) { return m1 = m1 * m2; }
    friend matrix& operator*=(matrix& m, const value_type& t)
    {
        for (usize i = 0; i < m.row; i++) {
            for (usize j = 0; j < m.column; j++) { m.table[i][j] *= t; }
        }
        return m;
    }
    friend matrix& operator/=(matrix& m, const value_type& t)
    {
        assert(t != 0);
        for (usize i = 0; i < m.row; i++) {
            for (usize j = 0; j < m.column; j++) { m.table[i][j] /= t; }
        }
        return m;
    }
    friend matrix& operator^=(matrix& m, const unsigned long long n) { return m = m ^ n; }
    friend std::ostream& operator<<(std::ostream& os, const matrix& m)
    {
        os << "[\n";
        for (usize i = 0; i < m.row; i++) {
            os << "[";
            for (usize j = 0; j < m.column; j++) { os << m[i][j] << ","; }
            os << "]\n";
        }
        return (os << "]\n");
    }
    static matrix id(const usize N)
    {
        matrix ans(N, N);
        for (usize i = 0; i < N; i++) { ans[i][i] = 1; }
        return ans;
    }
    const usize row, column;

private:
    std::vector<std::vector<value_type>> table;
};


template<typename T> T gcd(const T& a, const T& b) { return a < 0 ? gcd(-a, b) : b < 0 ? gcd(a, -b) : (a > b ? gcd(b, a) : a == 0 ? b : gcd(b % a, a)); }
template<typename T> T lcm(const T& a, const T& b) { return a / gcd(a, b) * b; }
template<typename T>
constexpr std::pair<T, T> extgcd(const T a, const T b)
{
    if (b == 0) { return std::pair<T, T>{1, 0}; }
    const auto g = gcd(a, b), da = std::abs(b) / g;
    const auto p = extgcd(b, a % b);
    const auto x = (da + p.second % da) % da, y = (g - a * x) / b;
    return {x, y};
}
template<typename T>
constexpr T inverse(const T a, const T mod) { return extgcd(a, mod).first; }
template<uint mod_value, bool dynamic = false>
class modint_base
{
public:
    template<typename UInt = uint>
    static std::enable_if_t<dynamic, const UInt> mod() { return mod_ref(); }
    template<typename UInt = uint>
    static constexpr std::enable_if_t<not dynamic, const UInt> mod() { return mod_value; }
    template<typename UInt = uint>
    static void set_mod(const std::enable_if_t<dynamic, const UInt> mod) { mod_ref() = mod, inv_ref() = {1, 1}; }
    modint_base() : v{0} {}
    modint_base(const ll val) : v{norm(static_cast<uint>(val % static_cast<ll>(mod()) + static_cast<ll>(mod())))} {}
    modint_base(const modint_base& n) : v{n()} {}
    explicit operator bool() const { return v != 0; }
    bool operator!() const { return not static_cast<bool>(*this); }
    modint_base& operator=(const modint_base& m) { return v = m(), (*this); }
    modint_base& operator=(const ll val) { return v = norm(uint(val % static_cast<ll>(mod()) + static_cast<ll>(mod()))), (*this); }
    friend modint_base operator+(const modint_base& m) { return m; }
    friend modint_base operator-(const modint_base& m) { return make(norm(mod() - m.v)); }
    friend modint_base operator+(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + m2.v)); }
    friend modint_base operator-(const modint_base& m1, const modint_base& m2) { return make(norm(m1.v + mod() - m2.v)); }
    friend modint_base operator*(const modint_base& m1, const modint_base& m2) { return make(static_cast<uint>(static_cast<ll>(m1.v) * static_cast<ll>(m2.v) % static_cast<ll>(mod()))); }
    friend modint_base operator/(const modint_base& m1, const modint_base& m2) { return m1 * inv(m2.v); }
    friend modint_base operator+(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) + val}; }
    friend modint_base operator-(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) - val}; }
    friend modint_base operator*(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }
    friend modint_base operator/(const modint_base& m, const ll val) { return modint_base{static_cast<ll>(m.v) * inv(val)}; }
    friend modint_base operator+(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) + val}; }
    friend modint_base operator-(const ll val, const modint_base& m) { return modint_base{-static_cast<ll>(m.v) + val}; }
    friend modint_base operator*(const ll val, const modint_base& m) { return modint_base{static_cast<ll>(m.v) * (val % static_cast<ll>(mod()))}; }
    friend modint_base operator/(const ll val, const modint_base& m) { return modint_base{val * inv(static_cast<ll>(m.v))}; }
    friend modint_base& operator+=(modint_base& m1, const modint_base& m2) { return m1 = m1 + m2; }
    friend modint_base& operator-=(modint_base& m1, const modint_base& m2) { return m1 = m1 - m2; }
    friend modint_base& operator*=(modint_base& m1, const modint_base& m2) { return m1 = m1 * m2; }
    friend modint_base& operator/=(modint_base& m1, const modint_base& m2) { return m1 = m1 / m2; }
    friend modint_base& operator+=(modint_base& m, const ll val) { return m = m + val; }
    friend modint_base& operator-=(modint_base& m, const ll val) { return m = m - val; }
    friend modint_base& operator*=(modint_base& m, const ll val) { return m = m * val; }
    friend modint_base& operator/=(modint_base& m, const ll val) { return m = m / val; }
    friend modint_base operator^(const modint_base& m, const ll n) { return power(m.v, n); }
    friend modint_base& operator^=(modint_base& m, const ll n) { return m = m ^ n; }
    friend bool operator==(const modint_base& m1, const modint_base& m2) { return m1.v == m2.v; }
    friend bool operator!=(const modint_base& m1, const modint_base& m2) { return not(m1 == m2); }
    friend bool operator==(const modint_base& m, const ll val) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }
    friend bool operator!=(const modint_base& m, const ll val) { return not(m == val); }
    friend bool operator==(const ll val, const modint_base& m) { return m.v == norm(static_cast<uint>(static_cast<ll>(mod()) + val % static_cast<ll>(mod()))); }
    friend bool operator!=(const ll val, const modint_base& m) { return not(m == val); }
    friend std::istream& operator>>(std::istream& is, modint_base& m)
    {
        ll v;
        return is >> v, m = v, is;
    }
    friend std::ostream& operator<<(std::ostream& os, const modint_base& m) { return os << m(); }
    uint operator()() const { return v; }
    static modint_base small_inv(const usize n)
    {
        auto& in = inv_ref();
        if (n < in.size()) { return in[n]; }
        for (usize i = in.size(); i <= n; i++) { in.push_back(-in[modint_base::mod() % i] * (modint_base::mod() / i)); }
        return in.back();
    }
    std::pair<ll, ll> quad() const
    {
        const auto ans = quad_r(v, mod());
        ll x = std::get<0>(ans), y = std::get<1>(ans);
        if (y < 0) { x = -x, y = -y; }
        return {x, y};
    }

private:
    static std::tuple<ll, ll, ll> quad_r(const ll r, const ll p)  // r = x/y (mod p), (x,y,z) s.t. x=yr+pz
    {
        if (std::abs(r) <= 1000) { return {r, 1, 0}; }
        ll nr = p % r, q = p / r;
        if (nr * 2LL >= r) { nr -= r, q++; }
        if (nr * 2LL <= -r) { nr += r, q--; }
        const auto sub = quad_r(nr, r);
        const ll x = std::get<0>(sub), z = std::get<1>(sub), y = std::get<2>(sub);
        return {x, y - q * z, z};
    }

    template<typename UInt = uint>
    static std::enable_if_t<dynamic, UInt&> mod_ref()
    {
        static UInt mod = 0;
        return mod;
    }
    static uint norm(const uint x) { return x < mod() ? x : x - mod(); }
    static modint_base make(const uint x)
    {
        modint_base m;
        return m.v = x, m;
    }
    static modint_base power(modint_base x, ull n)
    {
        modint_base ans = 1;
        for (; n; n >>= 1, x *= x) {
            if (n & 1) { ans *= x; }
        }
        return ans;
    }
    static modint_base inv(const ll v) { return v <= 2000000 ? small_inv(static_cast<usize>(v)) : modint_base{inverse(v, static_cast<ll>(mod()))}; }
    static std::vector<modint_base>& inv_ref()
    {
        static std::vector<modint_base> in{1, 1};
        return in;
    }
    uint v;
};
template<uint mod>
using modint = modint_base<mod, false>;
template<uint id>
using dynamic_modint = modint_base<id, true>;
int main()
{
    using mint   = modint<mod>;
    const auto N = in<int>(), W = in<int>();
    const auto K  = in<ll>();
    const auto as = in_v<int>({N});
    std::vector<mint> dp(W + 1, 0);
    dp[0] = 1;
    for (int i = 1; i <= W; i++) {
        for (int j = 0; j < N; j++) {
            if (i - as[j] < 0) { continue; }
            dp[i] += dp[i - as[j]];
        }
    }
    SHOW(dp);
    matrix<mint> trans(2 * W, 2 * W);  // -w,-(w-1),..-1, 0,1,2...,w-1
    for (int i = 0; i < W; i++) { trans[i + W][i] = 1; }
    for (int i = 0; i < W; i++) {
        for (int j = 0; j < W; j++) {
            if (i != 0 and j != 0) { continue; }
            for (int k = 0; k < N; k++) {
                const int pi = (j + W) - as[k];
                if (pi < i or pi >= W) { continue; }
                trans[i][j] += dp[pi - i];
            }
        }
    }
    for (int i = 0; i < W; i++) {
        for (int j = 0; j < W; j++) {
            if (i != 0 and j != 0) { continue; }
            for (int k = 0; k < N; k++) {
                const int pi = (j + 2 * W) - as[k];
                if (pi < i or pi >= W) { continue; }
                trans[i + W][j] += dp[pi - i];
            }
        }
    }
    SHOW(trans);
    const auto A = trans ^ K;
    outln(A[0][0]);
    return 0;
}
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