結果

問題 No.526 フィボナッチ数列の第N項をMで割った余りを求める
ユーザー morimariomorimario
提出日時 2020-12-18 17:33:47
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 20,356 bytes
コンパイル時間 2,163 ms
コンパイル使用メモリ 214,868 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-21 09:12:57
合計ジャッジ時間 2,762 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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 1 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 1 ms
5,376 KB
testcase_04 AC 1 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 1 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 3 ms
5,376 KB
testcase_13 AC 2 ms
5,376 KB
testcase_14 AC 1 ms
5,376 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 # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
using ll = long long; using ull = unsigned long long;
using pii = pair<int, int>; using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using pll = pair<ll, ll>; using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;
using pdd = pair<double, double>; using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using pbb = pair<bool, bool>; using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using pss = pair<string, string>; using vs = vector<string>; using vvs = vector<vs>; using vvvs = vector<vvs>;
#define rep2(counter, start, goal) for (int counter = (int)(start); counter < (int)(goal); ++counter)
#define rep(counter, goal) rep2(counter, 0, goal)
#define rep3(counter, start, goal) for (int counter = (int)(start); counter > (int)(goal); --counter)
#define rep0(times) for (int counter = 0; counter < (int)(times); ++counter)
#define all(container) begin(container), end(container)
template <typename T> bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; }
template <typename T> bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; }
void yn(bool flag) { cout << (flag ? "yes" : "no") << "\n"; }
void Yn(bool flag) { cout << (flag ? "Yes" : "No") << "\n"; }
void YN(bool flag) { cout << (flag ? "YES" : "NO") << "\n"; }
void set_prec(const int &digits) { cout << fixed << setprecision(digits); cerr << fixed << setprecision(digits); }
template <typename T> void pr(const T &obj) { cerr << obj; }
template <typename T, typename ...Ts> void pr(const T &first, const Ts &...rest) { pr(first); pr(", "); pr(rest...); }
template <typename S, typename T> void pr(const pair<S, T> &pair) { pr("("); pr(pair.first); pr(", "); pr(pair.second); pr(")"); }
template <typename T> void pr(const vector<T> &vec) { pr("{"); for (T obj : vec) { pr(obj); pr(", "); } pr("}"); }
template <typename T> void pr(const vector<vector<T>> &vv) { pr("\n"); rep(index, vv.size()) { pr("["); pr(index); pr("]: "); pr(vv[index]); pr("\n"); } }
template <typename T> void pr(const set<T> &vec) { pr("{"); for (T obj : vec) { pr(obj); pr(", "); } pr("}"); }
template <typename S, typename T> void pr(const map<S, T> &map) { pr("{"); for (pair<S, T> pair : map) { pr("("); pr(pair.first); pr(": "); pr(pair.second); pr("), "); } pr("}"); }
#define db(obj) cerr << #obj << ": "; pr(obj); cerr << " "
#define dl(obj) db(obj); cerr << "\n";
#define dm(...) cerr << "(" << #__VA_ARGS__ << "): ("; pr(__VA_ARGS__); cerr << ") "
#define dml(...) dm(__VA_ARGS__); cerr << "\n"
// Modint
namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m`
    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    for (long long a : {2, 7, 61}) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace internal

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }
    static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

//
using namespace atcoder;
using mint = modint;

template <typename T>
struct Matrix {
	int row, column;
	vector<vector<T>> val; // val[i][j]: i行j列成分
	Matrix(const int &_row, const int &_column) {
		row = _row;
		column = _column;
		val = vector<vector<T>>(row, vector<T>(column));
	}
	Matrix(const vector<vector<T>> &_val) {
		row = _val.size();
		column = _val[0].size();
		val = _val;
	}
	Matrix operator-() const {
		Matrix res{row, column};
		for (int i = 0; i < res.row; ++i) {
			for (int j = 0; j < res.column; ++j) {
				res.val[i][j] = -val[i][j];
			}
		}
		return res;
	}
};

// 零行列、単位行列
template <typename T>
Matrix<T> zero(const int &n) {
	Matrix<T> res{n, n};
	return res;
}

template <typename T>
Matrix<T> id(const int &n) {
	Matrix<T> res{n, n};
	for (int k = 0; k < n; ++k) {
		res.val[k][k] = 1;
	}
	return res;
}

// スカラー倍
template <typename T>
Matrix<T> operator*(const T &k, const Matrix<T> &A) {
	Matrix<T> res{A.row, A.column};
	for (int i = 0; i < res.row; ++i) {
		for (int j = 0; j < res.column; ++j) {
			res.val[i][j] = k * A.val[i][j];
		}
	}
	return res;
}

template <typename T>
Matrix<T> operator*(const Matrix<T> &A, const T &k) {
	return k * A;
}

// 加法
template <typename T>
Matrix<T> operator+(const Matrix<T> &left, const Matrix<T> &right) {
	assert(left.row == right.row && left.column == right.column);
	Matrix<T> res{left.row, left.column};
	for (int i = 0; i < res.row; ++i) {
		for (int j = 0; j < res.column; ++j) {
			res.val[i][j] = left.val[i][j] + right.val[i][j];
		}
	}
	return res;
}

template <typename T>
Matrix<T> operator-(const Matrix<T> &left, const Matrix<T> &right) {
	return left + (-right);
}

// 行列積
template <typename T>
Matrix<T> operator*(const Matrix<T> &left, const Matrix<T> &right) {
	assert (left.column == right.row);
	Matrix<T> res{left.row, right.column};
	for (int i = 0; i < res.row; ++i) {
		for (int j = 0; j < res.column; ++j) {
			for (int k = 0; k < left.column; ++k) {
				res.val[i][j] += left.val[i][k] * right.val[k][j];
			}
		}
	}
	return res;
}

// 行列累乗
template <typename T>
Matrix<T> pow(Matrix<T> A, long long m) { // m >= 0
	assert(A.row == A.column);
	Matrix<T> res = id<T>(A.row), X = A;
	while (m > 0) {
		if (m & 1) {
			res = res * X;
		}
		X = X * X;
		m >>= 1;
	}
	return res;
}

// debug
void show(Matrix<mint> A) {
	for (int i = 0; i < A.row; ++i) {
		for (int j = 0; j < A.column; ++j) {
			printf("(%d, %d): %d, ", i, j, A.val[i][j].val());
		}
		printf("\n");
	}
}

template <typename T>
void show(Matrix<T> A) {
	for (int i = 0; i < A.row; ++i) {
		for (int j = 0; j < A.column; ++j) {
			printf("(%d, %d): %d, ", i, j, A.val[i][j]);
		}
		printf("\n");
	}
}

int main() {
	int N, M; cin >> N >> M;
	mint::set_mod(M);
	Matrix<mint> A = {{{1, 1}, {1, 0}}};
	Matrix<mint> v = {{{1}, {0}}};
	Matrix<mint> x = pow(A, N - 1) * v;
	int ans = x.val[1][0].val();
	cout << ans << endl;
}
0