This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub maspypy/library
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "mod/first_mod_range_of_linear.hpp" #include "random/base.hpp" ll naive(ll L, ll R, ll a, ll b, ll mod) { FOR(x, mod) { FOR(y, L, R) { if (((a * x + b) - y) % mod == 0) return x; } } return -1; } void test() { ll K = 15; FOR(L, -K, K) { FOR(R, L, K) { FOR(mod, 1, K) { FOR(a, -K, K) { FOR(b, -K, K) { ll X = naive(L, R, a, b, mod); ll Y = first_mod_range_of_linear(L, R, a, b, mod); assert(X == Y); } } } } } K = 10000; FOR(100) { ll L = RNG(-K, K); ll R = RNG(-K, K); if (L > R) swap(L, R); ll mod = RNG(1, K); ll a = RNG(-K, K); ll b = RNG(-K, K); ll X = naive(L, R, a, b, mod); ll Y = first_mod_range_of_linear(L, R, a, b, mod); assert(X == Y); } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test(); solve(); return 0; }
#line 1 "test/1_mytest/first_mod_range_of_linear.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 1 "my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("Ofast,unroll-loops") // いまの CF だとこれ入れると動かない? // #pragma GCC target("avx2,popcnt") #include <bits/stdc++.h> using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'010'000'000; template <> constexpr ll infty<ll> = 2'020'000'000'000'000'000; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000; template <> constexpr double infty<double> = infty<ll>; template <> constexpr long double infty<long double> = infty<ll>; using pi = pair<ll, ll>; using vi = vector<ll>; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T> T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template <typename T> T ceil(T x, T y) { return floor(x + y - 1, y); } template <typename T> T bmod(T x, T y) { return x - y * floor(x, y); } template <typename T> pair<T, T> divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template <typename T, typename U> T SUM(const vector<U> &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template <typename T> T POP(deque<T> &que) { T a = que.front(); que.pop_front(); return a; } template <typename T> T POP(pq<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(pqg<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(vc<T> &que) { T a = que.back(); que.pop_back(); return a; } template <typename F> ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc<int> s_to_vi(const string &S, char first_char) { vc<int> A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template <typename T> vector<int> argsort(const vector<T> &A) { vector<int> ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { vc<T> B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } template <typename T, typename... Vectors> void concat(vc<T> &first, const Vectors &... others) { vc<T> &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif #line 3 "test/1_mytest/first_mod_range_of_linear.test.cpp" #line 2 "mod/min_of_linear_segments.hpp" /* ax + b (x>=0) が最小となるところの情報を返す。 prefix min を更新する x 全体が、等差数列の和集合。次を返す。 ・等差数列の境界となる x_0, x_1, ..., x_n ・各境界の間での交差 dx_0, ..., dx_{n-1} */ pair<vc<int>, vc<int>> min_of_linear_segments(int a, int b, int mod) { assert(0 <= a && a < mod); assert(0 <= b && b < mod); vc<int> X = {0}; vc<int> DX; int g = gcd(a, mod); a /= g, b /= g, mod /= g; // p/q <= (mod-a)/mod <= r/s int p = 0, q = 1, r = 1, s = 1; int det_l = mod - a, det_r = a; int x = 0, y = b; while (y) { // upd r/s int k = det_r / det_l; det_r %= det_l; if (det_r == 0) { --k; det_r = det_l; } r += k * p; s += k * q; while (1) { int k = max(0, ceil(det_l - y, det_r)); if (det_l - k * det_r <= 0) break; det_l -= k * det_r; p += k * r; q += k * s; // p/q <= a/mod // (aq - pmod) = det_l を y から引く k = y / det_l; y -= k * det_l; x += q * k; X.eb(x); DX.eb(q); } k = det_l / det_r; det_l -= k * det_r; p += k * r; q += k * s; assert(min({p, q, r, s}) >= 0); } return {X, DX}; } #line 2 "mod/first_mod_range_of_linear.hpp" // ax+b in {L, ..., R-1} mod となる最小の x>=0 を返す // 例えば ax+b=1 なら ax+b in {-1} mod 2 のようにする // 存在しなければ -1 // L<0 や mod<=R も ok int first_mod_range_of_linear(ll L, ll R, ll a, ll b, int mod) { assert(L <= R); b -= L, R -= L; if (R >= mod) return 0; a = bmod<ll>(a, mod), b = bmod<ll>(b, mod); // ax+b<R if (b < R) return 0; auto [X, DX] = min_of_linear_segments(a, b, mod); FOR(i, len(DX)) { ll x1 = X[i], x2 = X[i + 1]; ll y2 = (a * x2 + b) % mod; if (y2 >= R) continue; ll y1 = (a * x1 + b) % mod; ll d = (y1 - y2) * DX[i] / (x2 - x1); ll k = floor(y1 - R, d) + 1; return x1 + k * DX[i]; } return -1; } #line 2 "random/base.hpp" u64 RNG_64() { static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL; x_ ^= x_ << 7; return x_ ^= x_ >> 9; } u64 RNG(u64 lim) { return RNG_64() % lim; } ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); } #line 6 "test/1_mytest/first_mod_range_of_linear.test.cpp" ll naive(ll L, ll R, ll a, ll b, ll mod) { FOR(x, mod) { FOR(y, L, R) { if (((a * x + b) - y) % mod == 0) return x; } } return -1; } void test() { ll K = 15; FOR(L, -K, K) { FOR(R, L, K) { FOR(mod, 1, K) { FOR(a, -K, K) { FOR(b, -K, K) { ll X = naive(L, R, a, b, mod); ll Y = first_mod_range_of_linear(L, R, a, b, mod); assert(X == Y); } } } } } K = 10000; FOR(100) { ll L = RNG(-K, K); ll R = RNG(-K, K); if (L > R) swap(L, R); ll mod = RNG(1, K); ll a = RNG(-K, K); ll b = RNG(-K, K); ll X = naive(L, R, a, b, mod); ll Y = first_mod_range_of_linear(L, R, a, b, mod); assert(X == Y); } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test(); solve(); return 0; }