結果
| 問題 | No.1584 Stones around Circle Pond |
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-07-02 23:01:30 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 29,409 bytes |
| コンパイル時間 | 2,937 ms |
| コンパイル使用メモリ | 186,560 KB |
| 実行使用メモリ | 32,720 KB |
| 最終ジャッジ日時 | 2024-06-29 12:53:03 |
| 合計ジャッジ時間 | 5,160 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
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
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 59 ms
32,188 KB |
| testcase_04 | AC | 2 ms
5,376 KB |
| testcase_05 | WA | - |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | AC | 2 ms
5,376 KB |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | WA | - |
| testcase_16 | AC | 3 ms
5,376 KB |
| testcase_17 | WA | - |
| testcase_18 | AC | 3 ms
5,376 KB |
| testcase_19 | AC | 3 ms
5,376 KB |
| testcase_20 | AC | 7 ms
5,376 KB |
| testcase_21 | AC | 4 ms
5,376 KB |
| testcase_22 | AC | 6 ms
5,376 KB |
| testcase_23 | AC | 2 ms
5,376 KB |
| testcase_24 | AC | 8 ms
5,376 KB |
| testcase_25 | AC | 4 ms
5,376 KB |
| testcase_26 | AC | 2 ms
5,376 KB |
| testcase_27 | AC | 4 ms
5,376 KB |
| testcase_28 | AC | 5 ms
5,376 KB |
| testcase_29 | AC | 2 ms
5,376 KB |
| testcase_30 | AC | 4 ms
5,376 KB |
| testcase_31 | AC | 12 ms
5,692 KB |
| testcase_32 | AC | 17 ms
7,504 KB |
| testcase_33 | AC | 7 ms
5,376 KB |
| testcase_34 | AC | 5 ms
5,376 KB |
| testcase_35 | AC | 7 ms
5,376 KB |
| testcase_36 | AC | 7 ms
5,376 KB |
| testcase_37 | AC | 3 ms
5,376 KB |
| testcase_38 | WA | - |
| testcase_39 | WA | - |
| testcase_40 | WA | - |
| testcase_41 | WA | - |
| testcase_42 | WA | - |
| testcase_43 | WA | - |
| testcase_44 | WA | - |
| testcase_45 | WA | - |
| testcase_46 | AC | 3 ms
5,376 KB |
| testcase_47 | WA | - |
| testcase_48 | AC | 5 ms
5,376 KB |
| testcase_49 | AC | 20 ms
11,688 KB |
| testcase_50 | AC | 34 ms
17,908 KB |
| testcase_51 | WA | - |
| testcase_52 | WA | - |
| testcase_53 | WA | - |
| testcase_54 | WA | - |
| testcase_55 | AC | 3 ms
5,376 KB |
| testcase_56 | AC | 3 ms
5,376 KB |
| testcase_57 | AC | 6 ms
5,376 KB |
| testcase_58 | WA | - |
| testcase_59 | WA | - |
| testcase_60 | WA | - |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#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 <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 lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
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##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> 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 <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &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 <typename Float = double, int DEPS = 30, bool Randomize = true> struct Simplex {
const Float EPS = Float(1.0) / (1LL << DEPS);
int N, M;
std::vector<int> shuffle_idx;
std::vector<int> idx;
std::vector<std::vector<Float>> mat;
int i_ch, j_ch;
private:
void _initialize(const std::vector<std::vector<Float>> &A, const std::vector<Float> &b, const std::vector<Float> &c) {
N = c.size(), M = A.size();
mat.assign(M + 2, std::vector<Float>(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<int> 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<std::vector<Float>> A, std::vector<Float> b, std::vector<Float> c) {
is_infty = infeasible = false;
if (Randomize) {
std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());
std::vector<std::pair<std::vector<Float>, 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<Float> x;
Float ans;
};
uint32_t rand_int() // XorShift random integer generator
{
static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123;
uint32_t t = x ^ (x << 11);
x = y;
y = z;
z = w;
return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}
double rand_double() { return (double)rand_int() / UINT32_MAX; }
void No() {
puts("No");
exit(0);
}
template <int md> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
using lint = long long;
MDCONST static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val;
MDCONST ModInt() : val(0) {}
MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; }
MDCONST ModInt(lint v) { _setval(v % md + md); }
MDCONST explicit operator bool() const { return val != 0; }
MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); }
MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); }
MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); }
MDCONST ModInt operator-() const { return ModInt()._setval(md - val); }
MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); }
friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); }
friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); }
friend MDCONST ModInt operator/(lint a, const ModInt &x) {
return ModInt()._setval(a % md * x.inv() % md);
}
MDCONST bool operator==(const ModInt &x) const { return val == x.val; }
MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }
MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
MDCONST ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static std::vector<ModInt> facs, facinvs, invs;
MDCONST static void _precalculation(int N) {
int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
MDCONST lint inv() const {
if (this->val < std::min(md >> 1, 1 << 21)) {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val].val;
} else {
return this->pow(md - 2).val;
}
}
MDCONST ModInt fac() const {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val];
}
MDCONST ModInt facinv() const {
while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val];
}
MDCONST ModInt doublefac() const {
lint k = (this->val + 1) / 2;
return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
MDCONST ModInt nCr(const ModInt &r) const {
return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();
}
MDCONST ModInt nPr(const ModInt &r) const {
return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv();
}
ModInt sqrt() const {
if (val == 0) return 0;
if (md == 2) return val;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val, md - x.val));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
template <typename T> struct matrix {
int H, W;
std::vector<T> elem;
typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }
inline T &at(int i, int j) { return elem[i * W + j]; }
inline T get(int i, int j) const { return elem[i * W + j]; }
int height() const { return H; }
int width() const { return W; }
std::vector<std::vector<T>> vecvec() const {
std::vector<std::vector<T>> ret(H);
for (int i = 0; i < H; i++) {
std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));
}
return ret;
}
operator std::vector<std::vector<T>>() const { return vecvec(); }
matrix() = default;
matrix(int H, int W) : H(H), W(W), elem(H * W) {}
matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {
for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));
}
static matrix Identity(int N) {
matrix ret(N, N);
for (int i = 0; i < N; i++) ret.at(i, i) = 1;
return ret;
}
matrix operator-() const {
matrix ret(H, W);
for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];
return ret;
}
matrix operator*(const T &v) const {
matrix ret = *this;
for (auto &x : ret.elem) x *= v;
return ret;
}
matrix operator/(const T &v) const {
matrix ret = *this;
const T vinv = T(1) / v;
for (auto &x : ret.elem) x *= vinv;
return ret;
}
matrix operator+(const matrix &r) const {
matrix ret = *this;
for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];
return ret;
}
matrix operator-(const matrix &r) const {
matrix ret = *this;
for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];
return ret;
}
matrix operator*(const matrix &r) const {
matrix ret(H, r.W);
for (int i = 0; i < H; i++) {
for (int k = 0; k < W; k++) {
for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);
}
}
return ret;
}
matrix &operator*=(const T &v) { return *this = *this * v; }
matrix &operator/=(const T &v) { return *this = *this / v; }
matrix &operator+=(const matrix &r) { return *this = *this + r; }
matrix &operator-=(const matrix &r) { return *this = *this - r; }
matrix &operator*=(const matrix &r) { return *this = *this * r; }
bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }
bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }
bool operator<(const matrix &r) const { return elem < r.elem; }
matrix pow(int64_t n) const {
matrix ret = Identity(H);
bool ret_is_id = true;
if (n == 0) return ret;
for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
if (!ret_is_id) ret *= ret;
if ((n >> i) & 1) ret *= (*this), ret_is_id = false;
}
return ret;
}
std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {
matrix x = *this;
while (n) {
if (n & 1) vec = x * vec;
x *= x;
n >>= 1;
}
return vec;
};
matrix transpose() const {
matrix ret(W, H);
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);
}
return ret;
}
// Gauss-Jordan elimination
// - Require inverse for every non-zero element
// - Complexity: O(H^2 W)
template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>
static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
int piv = -1;
for (int j = h; j < mtr.H; j++) {
if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c)))) piv = j;
}
return piv;
}
template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>
static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {
for (int j = h; j < mtr.H; j++) {
if (mtr.get(j, c)) return j;
}
return -1;
}
matrix gauss_jordan() const {
int c = 0;
matrix mtr(*this);
std::vector<int> ws;
ws.reserve(W);
for (int h = 0; h < H; h++) {
if (c == W) break;
int piv = choose_pivot(mtr, h, c);
if (piv == -1) {
c++;
h--;
continue;
}
if (h != piv) {
for (int w = 0; w < W; w++) {
std::swap(mtr[piv][w], mtr[h][w]);
mtr.at(piv, w) *= -1; // To preserve sign of determinant
}
}
ws.clear();
for (int w = c; w < W; w++) {
if (mtr.at(h, w) != 0) ws.emplace_back(w);
}
const T hcinv = T(1) / mtr.at(h, c);
for (int hh = 0; hh < H; hh++)
if (hh != h) {
const T coeff = mtr.at(hh, c) * hcinv;
for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;
mtr.at(hh, c) = 0;
}
c++;
}
return mtr;
}
int rank_of_gauss_jordan() const {
for (int i = H * W - 1; i >= 0; i--) {
if (elem[i]) return i / W + 1;
}
return 0;
}
T determinant_of_upper_triangle() const {
T ret = 1;
for (int i = 0; i < H; i++) ret *= get(i, i);
return ret;
}
int inverse() {
assert(H == W);
std::vector<std::vector<T>> ret = Identity(H), tmp = *this;
int rank = 0;
for (int i = 0; i < H; i++) {
int ti = i;
while (ti < H and tmp[ti][i] == 0) ti++;
if (ti == H) {
continue;
} else {
rank++;
}
ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);
T inv = T(1) / tmp[i][i];
for (int j = 0; j < W; j++) ret[i][j] *= inv;
for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;
for (int h = 0; h < H; h++) {
if (i == h) continue;
const T c = -tmp[h][i];
for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;
for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;
}
}
*this = ret;
return rank;
}
friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {
assert(m.W == int(v.size()));
std::vector<T> ret(m.H);
for (int i = 0; i < m.H; i++) {
for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];
}
return ret;
}
friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {
assert(int(v.size()) == m.H);
std::vector<T> ret(m.W);
for (int i = 0; i < m.H; i++) {
for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);
}
return ret;
}
std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }
std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }
friend std::ostream &operator<<(std::ostream &os, const matrix &x) {
os << "[(" << x.H << " * " << x.W << " matrix)";
os << "\n[column sums: ";
for (int j = 0; j < x.W; j++) {
T s = 0;
for (int i = 0; i < x.H; i++) s += x.get(i, j);
os << s << ",";
}
os << "]";
for (int i = 0; i < x.H; i++) {
os << "\n[";
for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";
os << "]";
}
os << "]\n";
return os;
}
friend std::istream &operator>>(std::istream &is, matrix &x) {
for (auto &v : x.elem) is >> v;
return is;
}
};
// Solve Ax = b for T = ModInt<PRIME>
// - retval: {one of the solution, {freedoms}} (if solution exists)
// {{}, {}} (otherwise)
// Complexity:
// - Yield one of the possible solutions: O(H^2 W) (H: # of eqs., W: # of variables)
// - Enumerate all of the bases: O(HW(H + W))
template <typename T>
std::pair<std::vector<T>, std::vector<std::vector<T>>> system_of_linear_equations(matrix<T> A, std::vector<T> b) {
int H = A.H, W = A.W;
matrix<T> M(H, W + 1);
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) M[i][j] = A[i][j];
M[i][W] = b[i];
}
M = M.gauss_jordan();
std::vector<int> ss(W, -1);
for (int i = 0; i < H; i++) {
int j = 0;
while (j <= W and M[i][j] == 0) j++;
if (j == W) { // No solution
return {{}, {}};
}
if (j < W) ss[j] = i;
}
std::vector<T> x(W);
std::vector<std::vector<T>> D;
for (int j = 0; j < W; j++) {
if (ss[j] == -1) {
std::vector<T> d(W);
d[j] = 1;
for (int jj = 0; jj < j; jj++) {
if (ss[jj] != -1) d[jj] = -M[ss[jj]][j] / M[ss[jj]][jj];
}
D.emplace_back(d);
} else
x[j] = M[ss[j]][W] / M[ss[j]][j];
}
return std::make_pair(x, D);
}
// CUT begin
// Solve ax+by=gcd(a, b)
template <typename Int> Int extgcd(Int a, Int b, Int &x, Int &y) {
Int d = a;
if (b != 0) {
d = extgcd(b, a % b, y, x), y -= (a / b) * x;
} else {
x = 1, y = 0;
}
return d;
}
// Calculate a^(-1) (MOD m) s if gcd(a, m) == 1
// Calculate x s.t. ax == gcd(a, m) MOD m
template <typename Int> Int mod_inverse(Int a, Int m) {
Int x, y;
extgcd<Int>(a, m, x, y);
x %= m;
return x + (x < 0) * m;
}
// Require: 1 <= b
// return: (g, x) s.t. g = gcd(a, b), xa = g MOD b, 0 <= x < b/g
template <typename Int> constexpr std::pair<Int, Int> inv_gcd(Int a, Int b) {
a %= b;
if (a < 0) a += b;
if (a == 0) return {b, 0};
Int s = b, t = a, m0 = 0, m1 = 1;
while (t) {
Int u = s / t;
s -= t * u, m0 -= m1 * u;
auto tmp = s;
s = t, t = tmp, tmp = m0, m0 = m1, m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
template <typename Int> constexpr std::pair<Int, Int> crt(const std::vector<Int> &r, const std::vector<Int> &m) {
assert(r.size() == m.size());
int n = int(r.size());
// Contracts: 0 <= r0 < m0
Int r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
Int r1 = r[i] % m[i], m1 = m[i];
if (r1 < 0) r1 += m1;
if (m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
Int g, im;
std::tie(g, im) = inv_gcd<Int>(m0, m1);
Int u1 = m1 / g;
if ((r1 - r0) % g) return {0, 0};
Int x = (r1 - r0) / g % u1 * im % u1;
r0 += x * m0;
m0 *= u1;
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
template <int MOD>
vector<ModInt<MOD>> solve(int N, int L, vector<vector<int>> dist, vector<int> B) {
using mint = ModInt<MOD>;
matrix<mint> mat(N * 2, N + 1);
vector<mint> vec(B.size());
REP(i, B.size()) vec[i] = B[i];
REP(i, N * 2) {
REP(j, N) {
mat[i][j] = dist[i][j];
}
mat[i][N] = L;
}
dbg(mat);
dbg(vec);
auto [sol, freedom] = system_of_linear_equations(mat, vec);
dbg(sol);
return sol;
};
int main() {
int N, L;
cin >> N >> L;
vector<int> d(N);
cin >> d;
REP(i, N) d.push_back(d[i] + L);
vector<int> B(N * 2);
cin >> B;
vector dist(N * 2, vector<int>(N * 2));
REP(i, dist.size()) REP(j, dist[i].size()) {
auto dd = abs(d[i] - d[j]);
dist[i][j] = min(dd, L * 2 - dd);
}
dbg(dist);
constexpr int MOD1 = 1000000007;
constexpr int MOD2 = 1000000009;
constexpr lint m1m2 = lint(MOD1) * MOD2;
auto s1 = solve<MOD1>(N, L, dist, B);
auto s2 = solve<MOD2>(N, L, dist, B);
dbg(s1);
dbg(s2);
if (s1.empty()) No();
vector<lint> s(s1.size());
REP(i, s.size()) {
if (s1[i].val == s2[i].val) s[i] = s1[i].val;
else s[i] = -(-s1[i]).val;
auto [r, m] = crt<lint>(vector<lint>{s1[i].val, s2[i].val}, vector<lint>{MOD1, MOD2});
r = r * (m1m2 / m);
m = m1m2;
if (r > 1e12) {
dbg(r);
dbg(m);
r = -((m - r) % m);
}
s[i] = r;
}
dbg(s);
lint su = 0;
REP(i, N) su += abs(s[i]);
if (su > s.back()) No();
puts("Yes");
return 0;
using Float = double;
vector<vector<Float>> A;
vector<Float> b, c(N + 1);
dbg(d);
REP(i, N * 2) {
vector<Float> a(N + 1);
REP(j, N) {
a[j] = dist[i][j] - L;
}
a.back() = L;
A.push_back(a);
b.push_back(B[i]);
for (auto &x : a) x = -x;
A.push_back(a);
b.push_back(-B[i]);
}
dbg(A);
dbg(b);
dbg(c);
Simplex<Float, 20, false> simplex(A, b, c);
dbg(simplex.infeasible);
dbg(simplex.x);
if (simplex.infeasible) No();
for (auto x : simplex.x) {
if (abs(x - llround(x)) > 1e-5) No();
}
puts("Yes");
}