結果

問題 No.2989 Fibonacci Prize
ユーザー minato
提出日時 2024-12-14 02:39:38
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 66 ms / 2,000 ms
コード長 22,145 bytes
コンパイル時間 2,345 ms
コンパイル使用メモリ 190,112 KB
実行使用メモリ 14,788 KB
最終ジャッジ日時 2024-12-14 02:39:43
合計ジャッジ時間 5,155 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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ファイルパターン 結果
sample AC * 3
other AC * 77
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 #
プレゼンテーションモードにする

#line 1 "library-cpp/other/template.hpp"
// clang-format off
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#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 <optional>
#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 uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using maxheap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP0(n) for (auto minato = decay_t<decltype(n)>{}; minato < (n); ++minato)
#define REP1(i, n) for (auto i = decay_t<decltype(n)>{}; (i) < (n); (i)++)
#define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, name, ...) name
#define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t<decltype(n)>{}; (i)--)
#define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
template <class Container> int SZ(const Container& v) { return int(v.size()); }
template <class T> void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T> T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template <class T> T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template <class T> T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T(0)); }
template <class T> T ABS(T x) { return max(x, -x); }
template <class T> constexpr T POW(T x, ull n) { T ret = 1; while (n > 0) { if (n & 1) ret *= x; x *= x; n >>= 1; } return ret; }
template <class T> constexpr T POW(T x, ull n, T mod) { T ret = 1; while (n > 0) { if (n & 1) ret = ret * x % mod; x = x * x % mod; n >>= 1; } return 
    ret; }
constexpr long long floor_div(long long n, long long d) { return n / d - ((n ^ d) < 0 && n % d); }
template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
int popcount(ull x) { return __builtin_popcountll(x); }
int kthbit(ull x, int k) { return (x >> k) & 1; }
int popparity(ull x) { return __builtin_parityll(x); }
int parity_sign(ull x) { return (x & 1) ? -1 : 1; }
constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
template <typename S> void rearrange(const vector<S>& id) { (void)id; }
template <typename S, typename T> void rearrange_exec(const vector<S>& id, vector<T>& v) { vector<T> w(v.size()); for (size_t i = 0; i < id.size(); i
    ++) { w[i] = v[id[i]]; } v.swap(w); }
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S>& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange
    (id, tail...); }
template <class T>
vector<vector<T>> rot90(const vector<vector<T>>& v) {
    int n = v.size(), m = v[0].size();
    vector<vector<T>> ret(m, vector<T>(n));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            ret[m - 1 - j][i] = v[i][j];
        }
    }
    return ret;
}
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template <class T> vector<T> &operator++(vector<T>& v) { for (auto& e : v) { e++; } return v;} 
template <class T> vector<T> operator++(vector<T>& v, int) { auto res = v; for (auto& e : v) { e++; } return res; }
template <class T> vector<T> &operator--(vector<T>& v) { for (auto& e : v) { e--; } return v; }
template <class T> vector<T> operator--(vector<T>& v, int) { auto res = v; for (auto& e : v) { e--; } return res; }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x) { return pair<T1, T2>(-x.first, -x.second); }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first - y.first, x.second 
    - y.second); }
template <class T1, class T2> pair<T1, T2> operator+(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first + y.first, x.second 
    + y.second); }
template <class T1, class T2> pair<T1, T2> operator+=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l + r; }
template <class T1, class T2> pair<T1, T2> operator-=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l - r; }
constexpr char ln = '\n';
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
void YES(bool t = true) { cout << YESNO[t] << "\n"; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
void No(bool t = 1) { Yes(!t); }
template <class T> void drop(T x) { cout << x << "\n"; exit(0); }
#define INT(...)     \
    int __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    IN(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    IN(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LDB(...)             \
    long double __VA_ARGS__; \
    IN(__VA_ARGS__)
#define VEC(type, name, size) \
    vector<type> name(size);  \
    IN(name)
#define VEC2(type, name1, name2, size)     \
    vector<type> name1(size), name2(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size)           \
    vector<type> name1(size), name2(size), name3(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size)                 \
    vector<type> name1(size), name2(size), name3(size), name4(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, N, M)                       \
    vector<vector<type>> name(N, vector<type>(M)); \
    IN(name)
template <class T> void scan(T& a) { cin >> a; }
template <class T> void scan(vector<T>& a) { for (auto& i : a) scan(i); }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); }
std::vector<std::vector<int>> read_graph(int N, int M) {
    std::vector<std::vector<int>> g(N);
    for (int i = 0; i < M; i++) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        g[a].emplace_back(b);
        g[b].emplace_back(a);
    }
    return g;
}
std::vector<std::vector<int>> read_tree(int N) { return read_graph(N, N - 1); }
void print() { cout << "\n"; }
template <class T> void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << 
    *it; } print(); }
template <class T, class... Args> void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p);
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t);
template <class T> ostream& operator<<(ostream& os, vector<T> v);
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a);
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]);
template <class Key> ostream& operator<<(ostream& os, set<Key> s);
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp);
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s);
template <class T> ostream& operator<<(ostream& os, queue<T> q);
template <class T> ostream& operator<<(ostream& os, deque<T> q);
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q);
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q);
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); 
    debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << 
    ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{";  { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) 
    { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) 
    }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top
    (); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << 
    debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
void debug_table(const std::vector<std::vector<int>>& table) {
    for (const auto& row : table) {
        for (const auto& cell : row) {
            cerr << cell << "\t";
        }
        cerr << endl;
    }
}
#else
#define debug(...) (void(0))
void debug_table(const std::vector<std::vector<int>>& table) { (void)table; }
#endif
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////
// clang-format on
#line 2 "library-cpp/mod/DynamicModInt.hpp"
struct DynamicModInt {
    using Mint = DynamicModInt;
  public:
    static int mod() {
        return int(umod());
    }
    static void set(int MOD) {
        umod() = (unsigned int)MOD;
        im() = (unsigned long long)(-1) / umod() + 1;
    }
    static Mint raw(int v) {
        Mint x;
        x._v = v;
        return x;
    }
    DynamicModInt() : _v(0) {
    }
    DynamicModInt(long long v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    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) {
        unsigned long long z = _v;
        z *= rhs._v;
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im()) >> 64);
        _v = (unsigned int)(z - x * umod());
        if (umod() <= _v) _v += umod();
        return *this;
    }
    Mint& operator^=(long long n) {
        Mint x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    Mint& operator/=(const Mint& rhs) {
        return *this = *this * rhs.inv();
    }
    Mint operator+() const {
        return *this;
    }
    Mint operator-() const {
        return Mint() - *this;
    }
    explicit operator bool() const {
        return _v != 0;
    }
    Mint pow(long long n) const {
        Mint r = *this;
        r ^= n;
        return r;
    }
    Mint inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (;;) {
            t = a / b;
            a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return Mint(b * z);
            }
            y -= t * z;
            t = b / a;
            b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return Mint(a * y);
            }
            z -= t * y;
        }
    }
    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 Mint operator^(const Mint& lhs, long long 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;
    }
    friend Mint operator+(long long lhs, const Mint& rhs) {
        return (Mint(lhs) += rhs);
    }
    friend Mint operator-(long long lhs, const Mint& rhs) {
        return (Mint(lhs) -= rhs);
    }
    friend Mint operator*(long long lhs, const Mint& rhs) {
        return (Mint(lhs) *= rhs);
    }
    friend ostream& operator<<(ostream& os, const Mint& M) {
        return os << M._v;
    }
    friend istream& operator>>(istream& is, Mint& M) {
        long long x;
        is >> x;
        M = x;
        return is;
    }
  private:
    unsigned int _v;
    static unsigned long long& im() {
        static unsigned long long im = 0;
        return im;
    }
    static unsigned int& umod() {
        static unsigned int m = 0;
        return m;
    }
};
#line 2 "library-cpp/math/SquareMatrix.hpp"
#line 8 "library-cpp/math/SquareMatrix.hpp"
template <class T, int N> struct SquareMatrix {
    using Mat = std::array<std::array<T, N>, N>;
    int n;
    Mat A;
    SquareMatrix() : SquareMatrix(N) {
    }
    SquareMatrix(int n_) : n(n_), A({}) {
        assert(0 <= n and n <= N);
    }
    SquareMatrix(int n_, std::vector<std::vector<T>> v) : n(n_) {
        assert(n == (int)v.size());
        for (int i = 0; i < n; i++) {
            assert(n == (int)v[i].size());
            for (int j = 0; j < n; j++) {
                A[i][j] = v[i][j];
            }
        }
    }
    int size() const {
        return n;
    }
    const std::array<T, N>& operator[](int i) const {
        assert(i < n);
        return A[i];
    }
    std::array<T, N>& operator[](int i) {
        assert(i < n);
        return A[i];
    }
    static SquareMatrix mul_identity(int n_) {
        SquareMatrix I(n_);
        for (int i = 0; i < n_; i++) I[i][i] = 1;
        return I;
    }
    SquareMatrix& operator+=(const SquareMatrix& B) {
        assert(B.size() == n);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                (*this)[i][j] += B[i][j];
            }
        }
        return *this;
    }
    SquareMatrix& operator-=(const SquareMatrix& B) {
        assert(B.size() == n);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                (*this)[i][j] -= B[i][j];
            }
        }
        return *this;
    }
    SquareMatrix operator*(const SquareMatrix& B) const {
        assert(B.size() == n);
        SquareMatrix C(n);
        for (int i = 0; i < n; i++) {
            for (int k = 0; k < n; k++) {
                for (int j = 0; j < n; j++) {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
            }
        }
        return C;
    }
    SquareMatrix operator^(long long k) const {
        assert(k >= 0);
        SquareMatrix ret = mul_identity(n);
        SquareMatrix A = *this;
        while (k) {
            if (k & 1) ret = ret * A;
            A = A * A;
            k >>= 1;
        }
        return ret;
    }
    SquareMatrix operator+(const SquareMatrix& B) const {
        return SquareMatrix(*this) += B;
    }
    SquareMatrix operator-(const SquareMatrix& B) const {
        return SquareMatrix(*this) -= B;
    }
    SquareMatrix& operator*=(const SquareMatrix& B) {
        return *this = *this * B;
    }
    SquareMatrix& operator^=(long long k) {
        return *this = *this ^ k;
    }
    bool operator==(const SquareMatrix& B) const {
        return n == B.size() && A == B.A;
    }
    bool operator!=(const SquareMatrix& B) const {
        return n != B.size() || A != B.A;
    }
    T determinant() const {
        SquareMatrix B = *this;
        T ret = 1;
        for (int i = 0; i < n; i++) {
            int idx = -1;
            for (int j = i; j < n; j++) {
                if (B[j][i] != 0) idx = j;
            }
            if (idx == -1) return T(0);
            if (i != idx) {
                ret *= -1;
                std::swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T inv = T(1) / B[i][i];
            for (int j = 0; j < n; j++) {
                B[i][j] *= inv;
            }
            for (int j = i + 1; j < n; j++) {
                T a = B[j][i];
                if (a == 0) continue;
                for (int k = 0; k < n; k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return ret;
    }
#ifdef MINATO_LOCAL
    friend std::ostream& operator<<(std::ostream& os, const SquareMatrix& r) {
        os << "\n";
        os << "{\n";
        for (int i = 0; i < r.size(); i++) {
            os << "  {";
            for (int j = 0; j < r.size(); j++) {
                if (j) os << ", ";
                os << r[i][j];
            }
            os << "},\n";
        }
        os << "}\n";
        return os;
    }
#endif
};
#line 4 "A.cpp"
using mat = SquareMatrix<DynamicModInt, 2>;
void solve() {
    LL(N, M);
    auto slv = [&] {
        ll ans = 0;
        if (M == 1) {
            return N == 1 ? 2LL : 0;
        }
        if (M <= 100) {
            vec<ll> A(M);
            A[0] = 1;
            A[1] = 1;
            rep(i, 2, M) A[i] = A[i - 1] + A[i - 2];
            rep(r, M) {
                rep(l, r + 1) {
                    ll sum = 0;
                    rep(i, l, r + 1) sum += A[i];
                    if (sum % N == 0 and sum <= A[M - 1]) {
                        ans++;
                    }
                }
            }
            return ans;
        }
        if (N == 1) {
            ans += (M - 2) * (M - 1) / 2 + 3;
            return ans;
        }
        DynamicModInt::set(N);
        mat A;
        A[0][0] = 1;
        A[0][1] = 1;
        A[1][0] = 1;
        A[1][1] = 0;
        {
            mat B = A;
            B ^= M - 1;
            if (B[0][0] == 0) ans += 2;
        }
        {
            mat B = A;
            B ^= M - 2;
            if (B[0][0] == 0) ans++;
        }
        vec<ll> freq(N), S;
        S = {0, 1};
        ll a = 1 % N, b = 2 % N;
        do {
            ll c = (a + b) % N;
            ll d = (c + N - 1) % N;
            freq[d]++;
            S.push_back(d);
            a = b;
            b = c;
        } while (a != 1 % N or b != 2 % N);
        rep(2) S.pop_back();
        ll m = S.size();
        ll p = (M - 1) / m;
        ll q = (M - 1) % m;
        rep(i, N) freq[i] *= p;
        rep(i, q) freq[S[i]]++;
        rep(i, N) ans += freq[i] * (freq[i] - 1) / 2;
        return ans;
    };
    print(slv());
}
int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(7);
    int T = 1;
    // cin >> T;
    for (int test_case = 1; test_case <= T; test_case++) {
        // debug(test_case);
        solve();
    }
}
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