結果
問題 | No.2207 pCr検査 |
ユーザー |
|
提出日時 | 2023-02-03 21:31:28 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
TLE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 24,866 bytes |
コンパイル時間 | 3,155 ms |
コンパイル使用メモリ | 293,476 KB |
最終ジャッジ日時 | 2025-02-10 08:48:29 |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 20 TLE * 10 |
ソースコード
/*** date : 2023-02-03 21:31:21*/#define NDEBUGusing 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>// utilitynamespace 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, 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(vector<T> &v) {return next_permutation(begin(v), end(v));}template <typename T>using minpq = priority_queue<T, vector<T>, greater<T>>;} // namespace Nyaan// bit operationnamespace Nyaan {__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {return _mm_popcnt_u64(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// inoutnamespace 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...);}void outr() {}template <typename T, class... U, char sep = ' '>void outr(const T &t, const U &...u) {cout << t;outr(u...);}struct IoSetupNya {IoSetupNya() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetupnya;} // namespace Nyaan// debug#ifdef NyaanDebug#define trc(...) (void(0))#else#define trc(...) (void(0))#endif#ifdef NyaanLocal#define trc2(...) (void(0))#else#define trc2(...) (void(0))#endif// macro#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)namespace Nyaan {void solve();}int main() { Nyaan::solve(); }//struct Timer {chrono::high_resolution_clock::time_point st;Timer() { reset(); }void reset() { st = chrono::high_resolution_clock::now(); }chrono::milliseconds::rep elapsed() {auto ed = chrono::high_resolution_clock::now();return chrono::duration_cast<chrono::milliseconds>(ed - st).count();}};using namespace std;struct Barrett {using u32 = unsigned int;using i64 = long long;using u64 = unsigned long long;u32 m;u64 im;Barrett() : m(), im() {}Barrett(int n) : m(n), im(u64(-1) / m + 1) {}constexpr inline i64 quo(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;return m <= r ? x - 1 : x;}constexpr inline i64 rem(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;return m <= r ? r + m : r;}constexpr inline pair<i64, int> quorem(u64 n) {u64 x = u64((__uint128_t(n) * im) >> 64);u32 r = n - x * m;if (m <= r) return {x - 1, r + m};return {x, r};}constexpr inline i64 pow(u64 n, i64 p) {u32 a = rem(n), r = m == 1 ? 0 : 1;while (p) {if (p & 1) r = rem(u64(r) * a);a = rem(u64(a) * a);p >>= 1;}return r;}};struct ArbitraryModInt {int x;ArbitraryModInt() : x(0) {}ArbitraryModInt(int64_t y) {int z = y % get_mod();if (z < 0) z += get_mod();x = z;}ArbitraryModInt &operator+=(const ArbitraryModInt &p) {if ((x += p.x) >= get_mod()) x -= get_mod();return *this;}ArbitraryModInt &operator-=(const ArbitraryModInt &p) {if ((x += get_mod() - p.x) >= get_mod()) x -= get_mod();return *this;}ArbitraryModInt &operator*=(const ArbitraryModInt &p) {x = rem((unsigned long long)x * p.x);return *this;}ArbitraryModInt &operator/=(const ArbitraryModInt &p) {*this *= p.inverse();return *this;}ArbitraryModInt operator-() const { return ArbitraryModInt(-x); }ArbitraryModInt operator+(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) += p;}ArbitraryModInt operator-(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) -= p;}ArbitraryModInt operator*(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) *= p;}ArbitraryModInt operator/(const ArbitraryModInt &p) const {return ArbitraryModInt(*this) /= p;}bool operator==(const ArbitraryModInt &p) const { return x == p.x; }bool operator!=(const ArbitraryModInt &p) const { return x != p.x; }ArbitraryModInt inverse() const {int a = x, b = get_mod(), u = 1, v = 0, t;while (b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);}return ArbitraryModInt(u);}ArbitraryModInt pow(int64_t n) const {ArbitraryModInt ret(1), mul(x);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const ArbitraryModInt &p) {return os << p.x;}friend istream &operator>>(istream &is, ArbitraryModInt &a) {int64_t t;is >> t;a = ArbitraryModInt(t);return (is);}int get() const { return x; }inline unsigned int rem(unsigned long long p) { return barrett().rem(p); }static inline Barrett &barrett() {static Barrett b;return b;}static inline int &get_mod() {static int mod = 0;return mod;}static void set_mod(int md) {assert(0 < md && md <= (1LL << 30) - 1);get_mod() = md;barrett() = Barrett(md);}};template <typename T>struct Binomial {vector<T> f, g, h;Binomial(int MAX = 0) {assert(T::get_mod() != 0 && "Binomial<mint>()");f.resize(1, T{1});g.resize(1, T{1});h.resize(1, T{1});while (MAX >= (int)f.size()) extend();}void extend() {int n = f.size();int m = n * 2;f.resize(m);g.resize(m);h.resize(m);for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);g[m - 1] = f[m - 1].inverse();h[m - 1] = g[m - 1] * f[m - 2];for (int i = m - 2; i >= n; i--) {g[i] = g[i + 1] * T(i + 1);h[i] = g[i] * f[i - 1];}}T fac(int i) {if (i < 0) return T(0);while (i >= (int)f.size()) extend();return f[i];}T finv(int i) {if (i < 0) return T(0);while (i >= (int)g.size()) extend();return g[i];}T inv(int i) {if (i < 0) return -inv(-i);while (i >= (int)h.size()) extend();return h[i];}T C(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);return fac(n) * finv(n - r) * finv(r);}inline T operator()(int n, int r) { return C(n, r); }template <typename I>T multinomial(const vector<I>& r) {static_assert(is_integral<I>::value == true);int n = 0;for (auto& x : r) {if (x < 0) return T(0);n += x;}T res = fac(n);for (auto& x : r) res *= finv(x);return res;}template <typename I>T operator()(const vector<I>& r) {return multinomial(r);}T C_naive(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);T ret = T(1);r = min(r, n - r);for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);return ret;}T P(int n, int r) {if (n < 0 || n < r || r < 0) return T(0);return fac(n) * finv(n - r);}// [x^r] 1 / (1-x)^nT H(int n, int r) {if (n < 0 || r < 0) return T(0);return r == 0 ? 1 : C(n + r - 1, r);}};namespace inner {using i32 = int32_t;using u32 = uint32_t;using i64 = int64_t;using u64 = uint64_t;template <typename T>T gcd(T a, T b) {while (b) swap(a %= b, b);return a;}template <typename T>T inv(T a, T p) {T b = p, x = 1, y = 0;while (a) {T q = b / a;swap(a, b %= a);swap(x, y -= q * x);}assert(b == 1);return y < 0 ? y + p : y;}template <typename T, typename U>T modpow(T a, U n, T p) {T ret = 1 % p;for (; n; n >>= 1, a = U(a) * a % p)if (n & 1) ret = U(ret) * a % p;return ret;}} // namespace innernamespace my_rand {using i64 = long long;using u64 = unsigned long long;// [0, 2^64 - 1)u64 rng() {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;}// [l, r]i64 rng(i64 l, i64 r) {assert(l <= r);return l + rng() % (r - l + 1);}// [l, r)i64 randint(i64 l, i64 r) {assert(l < r);return l + rng() % (r - l);}// choose n numbers from [l, r) without overlappingvector<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);return ret;}// [0.0, 1.0)double rnd() { return rng() * 5.42101086242752217004e-20; }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_randusing my_rand::randint;using my_rand::randset;using my_rand::randshf;using my_rand::rnd;using my_rand::rng;struct ArbitraryLazyMontgomeryModInt {using mint = ArbitraryLazyMontgomeryModInt;using i32 = int32_t;using u32 = uint32_t;using u64 = uint64_t;static u32 mod;static u32 r;static u32 n2;static u32 get_r() {u32 ret = mod;for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;return ret;}static void set_mod(u32 m) {assert(m < (1 << 30));assert((m & 1) == 1);mod = m;n2 = -u64(m) % m;r = get_r();assert(r * mod == 1);}u32 a;ArbitraryLazyMontgomeryModInt() : a(0) {}ArbitraryLazyMontgomeryModInt(const int64_t &b): a(reduce(u64(b % mod + mod) * n2)){};static u32 reduce(const u64 &b) {return (b + u64(u32(b) * u32(-r)) * mod) >> 32;}mint &operator+=(const mint &b) {if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}mint &operator-=(const mint &b) {if (i32(a -= b.a) < 0) a += 2 * mod;return *this;}mint &operator*=(const mint &b) {a = reduce(u64(a) * b.a);return *this;}mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}mint operator+(const mint &b) const { return mint(*this) += b; }mint operator-(const mint &b) const { return mint(*this) -= b; }mint operator*(const mint &b) const { return mint(*this) *= b; }mint operator/(const mint &b) const { return mint(*this) /= b; }bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}mint operator-() const { return mint() - mint(*this); }mint pow(u64 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = ArbitraryLazyMontgomeryModInt(t);return (is);}mint inverse() const { return pow(mod - 2); }u32 get() const {u32 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static u32 get_mod() { return mod; }};typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;struct montgomery64 {using mint = montgomery64;using i64 = int64_t;using u64 = uint64_t;using u128 = __uint128_t;static u64 mod;static u64 r;static u64 n2;static u64 get_r() {u64 ret = mod;for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;return ret;}static void set_mod(u64 m) {assert(m < (1LL << 62));assert((m & 1) == 1);mod = m;n2 = -u128(m) % m;r = get_r();assert(r * mod == 1);}u64 a;montgomery64() : a(0) {}montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};static u64 reduce(const u128 &b) {return (b + u128(u64(b) * u64(-r)) * mod) >> 64;}mint &operator+=(const mint &b) {if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;return *this;}mint &operator-=(const mint &b) {if (i64(a -= b.a) < 0) a += 2 * mod;return *this;}mint &operator*=(const mint &b) {a = reduce(u128(a) * b.a);return *this;}mint &operator/=(const mint &b) {*this *= b.inverse();return *this;}mint operator+(const mint &b) const { return mint(*this) += b; }mint operator-(const mint &b) const { return mint(*this) -= b; }mint operator*(const mint &b) const { return mint(*this) *= b; }mint operator/(const mint &b) const { return mint(*this) /= b; }bool operator==(const mint &b) const {return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);}bool operator!=(const mint &b) const {return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);}mint operator-() const { return mint() - mint(*this); }mint pow(u128 n) const {mint ret(1), mul(*this);while (n > 0) {if (n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const mint &b) {return os << b.get();}friend istream &operator>>(istream &is, mint &b) {int64_t t;is >> t;b = montgomery64(t);return (is);}mint inverse() const { return pow(mod - 2); }u64 get() const {u64 ret = reduce(a);return ret >= mod ? ret - mod : ret;}static u64 get_mod() { return mod; }};typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;namespace fast_factorize {using u64 = uint64_t;template <typename mint>bool miller_rabin(u64 n, vector<u64> as) {if (mint::get_mod() != n) mint::set_mod(n);u64 d = n - 1;while (~d & 1) d >>= 1;mint e{1}, rev{int64_t(n - 1)};for (u64 a : as) {if (n <= a) break;u64 t = d;mint y = mint(a).pow(t);while (t != n - 1 && y != e && y != rev) {y *= y;t *= 2;}if (y != rev && t % 2 == 0) return false;}return true;}bool is_prime(u64 n) {if (~n & 1) return n == 2;if (n <= 1) return false;if (n < (1LL << 30))return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});elsereturn miller_rabin<montgomery64>(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});}template <typename mint, typename T>T pollard_rho(T n) {if (~n & 1) return 2;if (is_prime(n)) return n;if (mint::get_mod() != n) mint::set_mod(n);mint R, one = 1;auto f = [&](mint x) { return x * x + R; };auto rnd_ = [&]() { return rng() % (n - 2) + 2; };while (1) {mint x, y, ys, q = one;R = rnd_(), y = rnd_();T g = 1;constexpr int m = 128;for (int r = 1; g == 1; r <<= 1) {x = y;for (int i = 0; i < r; ++i) y = f(y);for (int k = 0; g == 1 && k < r; k += m) {ys = y;for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));g = inner::gcd<T>(q.get(), n);}}if (g == n) dog = inner::gcd<T>((x - (ys = f(ys))).get(), n);while (g == 1);if (g != n) return g;}exit(1);}using i64 = long long;vector<i64> inner_factorize(u64 n) {if (n <= 1) return {};u64 p;if (n <= (1LL << 30))p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n);elsep = pollard_rho<montgomery64, uint64_t>(n);if (p == n) return {i64(p)};auto l = inner_factorize(p);auto r = inner_factorize(n / p);copy(begin(r), end(r), back_inserter(l));return l;}vector<i64> factorize(u64 n) {auto ret = inner_factorize(n);sort(begin(ret), end(ret));return ret;}map<i64, i64> factor_count(u64 n) {map<i64, i64> mp;for (auto &x : factorize(n)) mp[x]++;return mp;}vector<i64> divisors(u64 n) {if (n == 0) return {};vector<pair<i64, i64>> v;for (auto &p : factorize(n)) {if (v.empty() || v.back().first != p) {v.emplace_back(p, 1);} else {v.back().second++;}}vector<i64> ret;auto f = [&](auto rc, int i, i64 x) -> void {if (i == (int)v.size()) {ret.push_back(x);return;}for (int j = v[i].second;; --j) {rc(rc, i + 1, x);if (j == 0) break;x *= v[i].first;}};f(f, 0, 1);sort(begin(ret), end(ret));return ret;}} // namespace fast_factorizeusing fast_factorize::divisors;using fast_factorize::factor_count;using fast_factorize::factorize;using fast_factorize::is_prime;/*** @brief 高速素因数分解(Miller Rabin/Pollard's Rho)* @docs docs/prime/fast-factorize.md*/using mint = ArbitraryModInt;using namespace Nyaan;void q() {ini(K);vp pe(K);in(pe);ll p = pe.back().first;vi kouho;rep1(i, p) kouho.push_back(i);Timer timer;for (int mod = TEN(9); mod <= TEN(9) + 1000; mod++) {if (timer.elapsed() > 2500) break;if (is_prime(mod) == false) continue;mint::set_mod(mod);Binomial<mint> C(p + 1);mint cur = 1;each2(pp, e, pe) cur *= mint{pp}.pow(e);vi nxt;each(r, kouho) {if (C(p, r) == cur) nxt.push_back(r);}swap(kouho, nxt);}if (sz(kouho))out(p, kouho.back());elseout(-1, -1);}void Nyaan::solve() {int t = 1;// in(t);while (t--) q();}