#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; 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##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &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) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif // Maximize cx s.t. Ax <= b, x >= 0 // Implementation idea: https://kopricky.github.io/code/Computation_Advanced/simplex.html // Refer to https://hitonanode.github.io/cplib-cpp/combinatorial_opt/simplex.hpp template struct Simplex { const Float EPS = Float(1.0) / (1LL << DEPS); int N, M; std::vector shuffle_idx; std::vector idx; std::vector> mat; int i_ch, j_ch; private: void _initialize(const std::vector> &A, const std::vector &b, const std::vector &c) { N = c.size(), M = A.size(); mat.assign(M + 2, std::vector(N + 2)); i_ch = M; for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) mat[i][j] = -A[i][j]; mat[i][N] = 1, mat[i][N + 1] = b[i]; if (mat[i_ch][N + 1] > mat[i][N + 1]) i_ch = i; } for (int j = 0; j < N; j++) mat[M][j] = c[j]; mat[M + 1][N] = -1; idx.resize(N + M + 1); std::iota(idx.begin(), idx.end(), 0); } inline Float abs_(Float x) noexcept { return x > -x ? x : -x; } void _solve() { std::vector jupd; for (nb_iter = 0, j_ch = N;; nb_iter++) { if (i_ch < M) { std::swap(idx[j_ch], idx[i_ch + N + 1]); mat[i_ch][j_ch] = Float(1) / mat[i_ch][j_ch]; jupd.clear(); for (int j = 0; j < N + 2; j++) { if (j != j_ch) { mat[i_ch][j] *= -mat[i_ch][j_ch]; if (abs_(mat[i_ch][j]) > EPS) jupd.push_back(j); } } for (int i = 0; i < M + 2; i++) { if (abs_(mat[i][j_ch]) < EPS or i == i_ch) continue; for (auto j : jupd) mat[i][j] += mat[i][j_ch] * mat[i_ch][j]; mat[i][j_ch] *= mat[i_ch][j_ch]; } } j_ch = -1; for (int j = 0; j < N + 1; j++) { if (j_ch < 0 or idx[j_ch] > idx[j]) { if (mat[M + 1][j] > EPS or (abs_(mat[M + 1][j]) < EPS and mat[M][j] > EPS)) j_ch = j; } } if (j_ch < 0) break; i_ch = -1; for (int i = 0; i < M; i++) { if (mat[i][j_ch] < -EPS) { if (i_ch < 0) { i_ch = i; } else if (mat[i_ch][N + 1] / mat[i_ch][j_ch] - mat[i][N + 1] / mat[i][j_ch] < -EPS) { i_ch = i; } else if (mat[i_ch][N + 1] / mat[i_ch][j_ch] - mat[i][N + 1] / mat[i][j_ch] < EPS and idx[i_ch] > idx[i]) { i_ch = i; } } } if (i_ch < 0) { is_infty = true; break; } } if (mat[M + 1][N + 1] < -EPS) { infeasible = true; return; } x.assign(N, 0); for (int i = 0; i < M; i++) { if (idx[N + 1 + i] < N) x[idx[N + 1 + i]] = mat[i][N + 1]; } ans = mat[M][N + 1]; } public: Simplex(std::vector> A, std::vector b, std::vector c) { is_infty = infeasible = false; if (Randomize) { std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count()); std::vector, Float>> Abs; for (unsigned i = 0; i < A.size(); i++) Abs.emplace_back(A[i], b[i]); std::shuffle(Abs.begin(), Abs.end(), rng); A.clear(), b.clear(); for (auto &&Ab : Abs) A.emplace_back(Ab.first), b.emplace_back(Ab.second); shuffle_idx.resize(c.size()); std::iota(shuffle_idx.begin(), shuffle_idx.end(), 0); std::shuffle(shuffle_idx.begin(), shuffle_idx.end(), rng); auto Atmp = A; auto ctmp = c; for (unsigned i = 0; i < A.size(); i++) { for (unsigned j = 0; j < A[i].size(); j++) A[i][j] = Atmp[i][shuffle_idx[j]]; } for (unsigned j = 0; j < c.size(); j++) c[j] = ctmp[shuffle_idx[j]]; } _initialize(A, b, c); _solve(); if (Randomize and x.size() == c.size()) { auto xtmp = x; for (unsigned j = 0; j < c.size(); j++) x[shuffle_idx[j]] = xtmp[j]; } } unsigned nb_iter; bool is_infty; bool infeasible; std::vector x; Float ans; }; void No() { puts("No"); exit(0); } int main() { int N, L; cin >> N >> L; vector d(N); cin >> d; REP(i, N) d.push_back(d[i] + L); vector Bin(N * 2); cin >> Bin; using Float = double; vector> A; vector b, c(N * 2); REP(i, N * 2) { vector a(N * 2); a[i] = -1; A.push_back(a); b.push_back(0); } dbg(d); REP(i, N * 2) { vector a(N * 2); REP(j, N * 2) { int t = abs(d[j] - d[i]); a[j] = min(t, L * 2 - t); } A.push_back(a); b.push_back(Bin[i]); for (auto &x : a) x = -x; A.push_back(a); b.push_back(-Bin[i]); } Simplex simplex(A, b, c); dbg(simplex.infeasible); dbg(simplex.x); if (simplex.infeasible) No(); for (auto x : simplex.x) { if (abs(x - llround(x)) > 0.001) No(); } puts("Yes"); }