#line 1 "verify/verify-unit-test/nimber.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
//
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
#line 64 "template/template.hpp"
// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(std::forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-unit-test/nimber.test.cpp"
//
#line 2 "math/nimber.hpp"
#line 2 "math/garner.hpp"
// input : a, M (0 < a < M)
// output : pair(g, x) s.t. g = gcd(a, M), xa = g (mod M), 0 <= x < b/g
template <typename uint>
pair<uint, uint> gcd_inv(uint a, uint M) {
assert(M != 0 && 0 < a);
a %= M;
uint b = M, s = 1, t = 0;
while (true) {
if (a == 0) return {b, t + M};
t -= b / a * s;
b %= a;
if (b == 0) return {a, s};
s -= a / b * t;
a %= b;
}
}
// 入力 : 0 <= rem[i] < mod[i], 1 <= mod[i]
// 存在するとき : return {rem, mod}
// 存在しないとき : return {0, 0}
template <typename T, typename U>
pair<unsigned long long, unsigned long long> garner(const vector<T>& rem,
const vector<U>& mod) {
assert(rem.size() == mod.size());
using u64 = unsigned long long;
u64 r0 = 0, m0 = 1;
for (int i = 0; i < (int)rem.size(); i++) {
assert(1 <= mod[i]);
assert(0 <= rem[i] && rem[i] < mod[i]);
u64 m1 = mod[i], r1 = rem[i] % m1;
if (m0 < m1) swap(r0, r1), swap(m0, m1);
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
u64 g, im;
tie(g, im) = gcd_inv(m0, m1);
u64 y = r0 < r1 ? r1 - r0 : r0 - r1;
if (y % g != 0) return {0, 0};
u64 u1 = m1 / g;
y = y / g % u1;
if (r0 > r1 && y != 0) y = u1 - y;
u64 x = y * im % u1;
r0 += x * m0;
m0 *= u1;
}
return {r0, m0};
}
/**
* @brief Garner's algorithm
*/
#line 4 "math/nimber.hpp"
namespace NimberImpl {
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
struct calc8 {
u16 dp[1 << 8][1 << 8];
constexpr calc8() : dp() {
dp[0][0] = dp[0][1] = dp[1][0] = 0;
dp[1][1] = 1;
for (int e = 1; e <= 3; e++) {
int p = 1 << e, q = p >> 1;
u16 ep = 1u << p, eq = 1u << q;
for (u16 i = 0; i < ep; i++) {
for (u16 j = i; j < ep; j++) {
if (i < eq && j < eq) continue;
if (min(i, j) <= 1u) {
dp[i][j] = dp[j][i] = i * j;
continue;
}
u16 iu = i >> q, il = i & (eq - 1);
u16 ju = j >> q, jl = j & (eq - 1);
u16 u = dp[iu][ju], l = dp[il][jl];
u16 ul = dp[iu ^ il][ju ^ jl];
u16 uq = dp[u][eq >> 1];
dp[i][j] = ((ul ^ l) << q) ^ uq ^ l;
dp[j][i] = dp[i][j];
}
}
}
}
} constexpr c8;
struct calc16 {
static constexpr u16 proot = 10279;
static constexpr u32 ppoly = 92191;
static constexpr int order = 65535;
u16 base[16], exp[(1 << 18) + 100];
int log[1 << 16];
private:
constexpr u16 d(u32 x) { return (x << 1) ^ (x < 32768u ? 0 : ppoly); }
constexpr u16 naive(u16 i, u16 j) {
if (min(i, j) <= 1u) return i * j;
u16 q = 8, eq = 1u << 8;
u16 iu = i >> q, il = i & (eq - 1);
u16 ju = j >> q, jl = j & (eq - 1);
u16 u = c8.dp[iu][ju];
u16 l = c8.dp[il][jl];
u16 ul = c8.dp[iu ^ il][ju ^ jl];
u16 uq = c8.dp[u][eq >> 1];
return ((ul ^ l) << q) ^ uq ^ l;
}
public:
constexpr calc16() : base(), exp(), log() {
base[0] = 1;
for (int i = 1; i < 16; i++) base[i] = naive(base[i - 1], proot);
exp[0] = 1;
for (int i = 1; i < order; i++) exp[i] = d(exp[i - 1]);
u16* pre = exp + order + 1;
pre[0] = 0;
for (int b = 0; b < 16; b++) {
int is = 1 << b, ie = is << 1;
for (int i = is; i < ie; i++) pre[i] = pre[i - is] ^ base[b];
}
for (int i = 0; i < order; i++) exp[i] = pre[exp[i]], log[exp[i]] = i;
int ie = 2 * order + 30;
for (int i = order; i < ie; i++) exp[i] = exp[i - order];
for (unsigned int i = ie; i < sizeof(exp) / sizeof(u16); i++) exp[i] = 0;
log[0] = ie + 1;
}
constexpr u16 prod(u16 i, u16 j) const { return exp[log[i] + log[j]]; }
// exp[3] = 2^{15} = 32768
constexpr u16 Hprod(u16 i, u16 j) const { return exp[log[i] + log[j] + 3]; }
constexpr u16 H(u16 i) const { return exp[log[i] + 3]; }
constexpr u16 H2(u16 i) const { return exp[log[i] + 6]; }
} constexpr c16;
u16 product16(u16 i, u16 j) { return c16.prod(i, j); }
constexpr u32 product32(u32 i, u32 j) {
u16 iu = i >> 16, il = i & 65535;
u16 ju = j >> 16, jl = j & 65535;
u16 l = c16.prod(il, jl);
u16 ul = c16.prod(iu ^ il, ju ^ jl);
u16 uq = c16.Hprod(iu, ju);
return (u32(ul ^ l) << 16) ^ uq ^ l;
}
// (+ : xor, x : nim product, * : integer product)
// i x j
// = (iu x ju + il x ju + iu x ji) * 2^{16}
// + (iu x ju x 2^{15}) + il x jl
// (assign ju = 2^{15}, jl = 0)
// = ((iu + il) x 2^{15}) * 2^{16} + (iu x 2^{15} x 2^{15})
constexpr u32 H(u32 i) {
u16 iu = i >> 16;
u16 il = i & 65535;
return (u32(c16.H(iu ^ il)) << 16) ^ c16.H2(iu);
}
constexpr u64 product64(u64 i, u64 j) {
u32 iu = i >> 32, il = i & u32(-1);
u32 ju = j >> 32, jl = j & u32(-1);
u32 l = product32(il, jl);
u32 ul = product32(iu ^ il, ju ^ jl);
u32 uq = H(product32(iu, ju));
return (u64(ul ^ l) << 32) ^ uq ^ l;
}
} // namespace NimberImpl
template <typename uint, uint (*prod)(uint, uint)>
struct NimberBase {
using N = NimberBase;
uint x;
NimberBase() : x(0) {}
NimberBase(uint _x) : x(_x) {}
static N id0() { return {}; }
static N id1() { return {1}; }
N& operator+=(const N& p) {
x ^= p.x;
return *this;
}
N& operator-=(const N& p) {
x ^= p.x;
return *this;
}
N& operator*=(const N& p) {
x = prod(x, p.x);
return *this;
}
N operator+(const N& p) const { return x ^ p.x; }
N operator-(const N& p) const { return x ^ p.x; }
N operator*(const N& p) const { return prod(x, p.x); }
bool operator==(const N& p) const { return x == p.x; }
bool operator!=(const N& p) const { return x != p.x; }
N pow(uint64_t n) const {
N a = *this, r = 1;
for (; n; a *= a, n >>= 1)
if (n & 1) r *= a;
return r;
}
friend ostream& operator<<(ostream& os, const N& p) { return os << p.x; }
// calculate log_a (b)
uint discrete_logarithm(N y) const {
assert(x != 0 && y != 0);
vector<uint> rem, mod;
for (uint p : {3, 5, 17, 257, 641, 65537, 6700417}) {
if (uint(-1) % p) continue;
uint q = uint(-1) / p;
uint STEP = 1;
while (4 * STEP * STEP < p) STEP *= 2;
// a^m = z を満たす 1 以上の整数 m を返す
auto inside = [&](N a, N z) -> uint {
unordered_map<uint, int> mp;
N big = 1, now = 1; // x^m
for (int i = 0; i < int(STEP); i++) {
mp[z.x] = i, z *= a, big *= a;
}
for (int step = 0; step < int(p + 10); step += STEP) {
now *= big;
if (mp.find(now.x) != mp.end()) return (step + STEP) - mp[now.x];
}
return uint(-1);
};
N xq = (*this).pow(q), yq = y.pow(q);
if (xq == 1 and yq == 1) continue;
if (xq == 1 and yq != 1) return uint(-1);
uint res = inside(xq, yq);
if (res == uint(-1)) return uint(-1);
rem.push_back(res % p);
mod.push_back(p);
}
return garner(rem, mod).first;
}
uint is_primitive_root() const {
if (x == 0) return false;
for (uint p : {3, 5, 17, 257, 641, 65537, 6700417}) {
if (uint(-1) % p != 0) continue;
if ((*this).pow(uint(-1) / p) == 1) return false;
}
return true;
}
};
using Nimber16 = NimberBase<uint16_t, NimberImpl::product16>;
using Nimber32 = NimberBase<uint32_t, NimberImpl::product32>;
using Nimber64 = NimberBase<uint64_t, NimberImpl::product64>;
using Nimber = Nimber64;
/**
* @brief Nim Product
* @docs docs/math/nimber.md
*/
#line 2 "misc/rng.hpp"
#line 2 "internal/internal-seed.hpp"
#line 4 "internal/internal-seed.hpp"
using namespace std;
namespace internal {
unsigned long long non_deterministic_seed() {
unsigned long long m =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
m ^= 9845834732710364265uLL;
m ^= m << 24, m ^= m >> 31, m ^= m << 35;
return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }
// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
return deterministic_seed();
#else
return non_deterministic_seed();
#endif
}
} // namespace internal
#line 4 "misc/rng.hpp"
namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;
// [0, 2^64 - 1)
u64 rng() {
static u64 _x = internal::seed();
return _x ^= _x << 7, _x ^= _x >> 9;
}
// [l, r]
i64 rng(i64 l, i64 r) {
assert(l <= r);
return l + rng() % u64(r - l + 1);
}
// [l, r)
i64 randint(i64 l, i64 r) {
assert(l < r);
return l + rng() % u64(r - l);
}
// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
assert(l <= r && n <= r - l);
unordered_set<i64> s;
for (i64 i = n; i; --i) {
i64 m = randint(l, r + 1 - i);
if (s.find(m) != s.end()) m = r - i;
s.insert(m);
}
vector<i64> ret;
for (auto& x : s) ret.push_back(x);
sort(begin(ret), end(ret));
return ret;
}
// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
assert(l < r);
return l + rnd() * (r - l);
}
template <typename T>
void randshf(vector<T>& v) {
int n = v.size();
for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}
} // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 7 "verify/verify-unit-test/nimber.test.cpp"
// 古い実装
namespace nimber {
using u64 = uint64_t;
u64 calc(u64, u64, int p, int pre);
struct Precalc {
u64 dp[256][256];
Precalc() {
for (int i = 0; i < 256; i++)
for (int j = 0; j <= i; j++) {
dp[i][j] = dp[j][i] = calc(i, j, 8, true);
}
}
} precalc;
u64 calc(u64 a, u64 b, int p = 64, int pre = false) {
if (min(a, b) <= 1) return a * b;
while (max(a, b) < 1ull << (p >> 1)) p >>= 1;
if (!pre && p <= 8) return precalc.dp[a][b];
p >>= 1;
u64 a1 = a >> p, a2 = a & ((1ull << p) - 1);
u64 b1 = b >> p, b2 = b & ((1ull << p) - 1);
u64 c = calc(a1, b1, p, pre);
u64 d = calc(a2, b2, p, pre);
u64 e = calc(a1 ^ a2, b1 ^ b2, p, pre);
return calc(c, 1ull << (p - 1), p, pre) ^ d ^ ((d ^ e) << p);
}
u64 nim_product(u64 a, u64 b) { return calc(a, b); }
} // namespace nimber
using nimber::nim_product;
using namespace Nyaan;
void Nyaan::solve() {
using namespace NimberImpl;
rep(i, 256) rep(j, 256) {
auto x1 = nim_product(i, j);
auto x2 = c8.dp[i][j];
auto x3 = c16.prod(i, j);
auto x4 = product32(i, j);
auto x5 = product64(i, j);
assert(x1 == x2);
assert(x1 == x3);
assert(x1 == x4);
assert(x1 == x5);
}
cerr << "256 OK" << endl;
rep(t, TEN(6)) {
u16 i = rng();
u16 j = rng();
auto x1 = nim_product(i, j);
auto x3 = c16.prod(i, j);
auto x4 = product32(i, j);
auto x5 = product64(i, j);
assert(x1 == x3);
assert(x1 == x4);
assert(x1 == x5);
}
cerr << "65536 OK" << endl;
rep(t, TEN(6)) {
u32 i = rng();
u32 j = rng();
auto x1 = nim_product(i, j);
auto x4 = product32(i, j);
auto x5 = product64(i, j);
assert(x1 == x4);
assert(x1 == x5);
}
cerr << "2^32 OK" << endl;
rep(t, TEN(6)) {
u64 i = rng();
u64 j = rng();
auto x1 = nim_product(i, j);
auto x5 = product64(i, j);
assert(x1 == x5);
}
cerr << "2^64 OK" << endl;
int a, b;
cin >> a >> b;
cout << a + b << endl;
}
verify/verify-unit-test/nimber.test.cpp