結果
| 問題 | No.2207 pCr検査 |
| ユーザー |
 maspy
|
| 提出日時 | 2023-02-03 21:59:24 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,249 ms / 3,000 ms |
| コード長 | 25,132 bytes |
| コンパイル時間 | 4,231 ms |
| コンパイル使用メモリ | 284,316 KB |
| 実行使用メモリ | 115,132 KB |
| 最終ジャッジ日時 | 2024-07-02 19:54:09 |
| 合計ジャッジ時間 | 22,566 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（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 | 3 ms
5,376 KB |
| testcase_02 | AC | 1,204 ms
111,852 KB |
| testcase_03 | AC | 653 ms
76,956 KB |
| testcase_04 | AC | 827 ms
84,064 KB |
| testcase_05 | AC | 1,119 ms
110,740 KB |
| testcase_06 | AC | 1,002 ms
104,616 KB |
| testcase_07 | AC | 627 ms
75,832 KB |
| testcase_08 | AC | 356 ms
41,336 KB |
| testcase_09 | AC | 851 ms
85,060 KB |
| testcase_10 | AC | 595 ms
73,692 KB |
| testcase_11 | AC | 881 ms
84,024 KB |
| testcase_12 | AC | 308 ms
41,264 KB |
| testcase_13 | AC | 158 ms
39,612 KB |
| testcase_14 | AC | 39 ms
12,440 KB |
| testcase_15 | AC | 301 ms
72,644 KB |
| testcase_16 | AC | 142 ms
39,268 KB |
| testcase_17 | AC | 223 ms
39,676 KB |
| testcase_18 | AC | 179 ms
37,732 KB |
| testcase_19 | AC | 93 ms
21,744 KB |
| testcase_20 | AC | 146 ms
37,336 KB |
| testcase_21 | AC | 314 ms
75,496 KB |
| testcase_22 | AC | 216 ms
13,696 KB |
| testcase_23 | AC | 211 ms
13,568 KB |
| testcase_24 | AC | 50 ms
11,884 KB |
| testcase_25 | AC | 125 ms
22,484 KB |
| testcase_26 | AC | 114 ms
21,444 KB |
| testcase_27 | AC | 221 ms
38,360 KB |
| testcase_28 | AC | 1,248 ms
115,008 KB |
| testcase_29 | AC | 1,242 ms
115,132 KB |
| testcase_30 | AC | 1,248 ms
115,132 KB |
| testcase_31 | AC | 1,249 ms
115,128 KB |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
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); }
// (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, typename U>
T ceil(T x, U y) {
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sum = 0;
for (auto &&a: A) sum += a;
return sum;
}
#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) {
assert(!que.empty());
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
assert(!que.empty());
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng) {
assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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;
tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
template <class T>
static auto check(T &&x) -> decltype(x.write(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};
struct has_read_impl {
template <class T>
static auto check(T &&x) -> decltype(x.read(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};
struct Scanner {
FILE *fp;
char line[(1 << 15) + 1];
size_t st = 0, ed = 0;
void reread() {
memmove(line, line + st, ed - st);
ed -= st;
st = 0;
ed += fread(line + ed, 1, (1 << 15) - ed, fp);
line[ed] = '\0';
}
bool succ() {
while (true) {
if (st == ed) {
reread();
if (st == ed) return false;
}
while (st != ed && isspace(line[st])) st++;
if (st != ed) break;
}
if (ed - st <= 50) {
bool sep = false;
for (size_t i = st; i < ed; i++) {
if (isspace(line[i])) {
sep = true;
break;
}
}
if (!sep) reread();
}
return true;
}
template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
while (true) {
size_t sz = 0;
while (st + sz < ed && !isspace(line[st + sz])) sz++;
ref.append(line + st, sz);
st += sz;
if (!sz || st != ed) break;
reread();
}
return true;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
ref = T(0);
while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
if (neg) ref = -ref;
return true;
}
template <typename T,
typename enable_if<has_read<T>::value>::type * = nullptr>
inline bool read_single(T &x) {
x.read();
return true;
}
bool read_single(double &ref) {
string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
bool read_single(char &ref) {
string s;
if (!read_single(s) || s.size() != 1) return false;
ref = s[0];
return true;
}
template <class T>
bool read_single(vector<T> &ref) {
for (auto &d: ref) {
if (!read_single(d)) return false;
}
return true;
}
template <class T, class U>
bool read_single(pair<T, U> &p) {
return (read_single(p.first) && read_single(p.second));
}
template <size_t N = 0, typename T>
void read_single_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
read_single(x);
read_single_tuple<N + 1>(t);
}
}
template <class... T>
bool read_single(tuple<T...> &tpl) {
read_single_tuple(tpl);
return true;
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
Printer(FILE *_fp) : fp(_fp) {}
~Printer() { flush(); }
static constexpr size_t SIZE = 1 << 15;
FILE *fp;
char line[SIZE], small[50];
size_t pos = 0;
void flush() {
fwrite(line, 1, pos, fp);
pos = 0;
}
void write(const char val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void write(T val) {
if (pos > (1 << 15) - 50) flush();
if (val == 0) {
write('0');
return;
}
if (val < 0) {
write('-');
val = -val; // todo min
}
size_t len = 0;
while (val) {
small[len++] = char(0x30 | (val % 10));
val /= 10;
}
for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
pos += len;
}
void write(const string s) {
for (char c: s) write(c);
}
void write(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write(s[i]);
}
void write(const double x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
write(s);
}
void write(const long double x) {
ostringstream oss;
oss << fixed << setprecision(15) << x;
string s = oss.str();
write(s);
}
template <typename T,
typename enable_if<has_write<T>::value>::type * = nullptr>
inline void write(T x) {
x.write();
}
template <class T>
void write(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
template <class T, class U>
void write(const pair<T, U> val) {
write(val.first);
write(' ');
write(val.second);
}
template <size_t N = 0, typename T>
void write_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { write(' '); }
const auto x = std::get<N>(t);
write(x);
write_tuple<N + 1>(t);
}
}
template <class... T>
bool write(tuple<T...> tpl) {
write_tuple(tpl);
return true;
}
template <class T, size_t S>
void write(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
void write(i128 val) {
string s;
bool negative = 0;
if (val < 0) {
negative = 1;
val = -val;
}
while (val) {
s += '0' + int(val % 10);
val /= 10;
}
if (negative) s += "-";
reverse(all(s));
if (len(s) == 0) s = "0";
write(s);
}
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
printer.write(head);
if (sizeof...(Tail)) printer.write(' ');
print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
scanner.read(head);
read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "/home/maspy/compro/library/mod/modint.hpp"
template <int mod>
struct modint {
int val;
constexpr modint(ll x = 0) noexcept {
if (0 <= x && x < mod)
val = x;
else {
x %= mod;
val = (x < 0 ? x + mod : x);
}
}
bool operator<(const modint &other) const {
return val < other.val;
} // To use std::map
modint &operator+=(const modint &p) {
if ((val += p.val) >= mod) val -= mod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += mod - p.val) >= mod) val -= mod;
return *this;
}
modint &operator*=(const modint &p) {
val = (int)(1LL * val * p.val % mod);
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint(-val); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(int64_t n) const {
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
#ifdef FASTIO
void write() { fastio::printer.write(val); }
void read() {
ll x;
fastio::scanner.read(x);
if (x < 0 || x >= mod) x %= mod;
if (x < 0) x += mod;
val += x;
}
#endif
static constexpr int get_mod() { return mod; }
};
struct ArbitraryModInt {
static constexpr bool is_modint = true;
int val;
ArbitraryModInt() : val(0) {}
ArbitraryModInt(int64_t y)
: val(y >= 0 ? y % get_mod()
: (get_mod() - (-y) % get_mod()) % get_mod()) {}
bool operator<(const ArbitraryModInt &other) const {
return val < other.val;
} // To use std::map<ArbitraryModInt, T>
static int &get_mod() {
static int mod = 0;
return mod;
}
static void set_mod(int md) { get_mod() = md; }
ArbitraryModInt &operator+=(const ArbitraryModInt &p) {
if ((val += p.val) >= get_mod()) val -= get_mod();
return *this;
}
ArbitraryModInt &operator-=(const ArbitraryModInt &p) {
if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod();
return *this;
}
ArbitraryModInt &operator*=(const ArbitraryModInt &p) {
long long a = (long long)val * p.val;
int xh = (int)(a >> 32), xl = (int)a, d, m;
asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod()));
val = m;
return *this;
}
ArbitraryModInt &operator/=(const ArbitraryModInt &p) {
*this *= p.inverse();
return *this;
}
ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); }
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 val == p.val; }
bool operator!=(const ArbitraryModInt &p) const { return val != p.val; }
ArbitraryModInt inverse() const {
int a = val, 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(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
#ifdef FASTIO
void write() { fastio::printer.write(val); }
void read() { fastio::scanner.read(val); }
#endif
};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (int(dat.size()) <= n) {
int k = dat.size();
auto q = (mod + k - 1) / k;
int r = k * q - mod;
dat.emplace_back(dat[r] * mint(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {1, 1};
assert(0 <= n);
if (n >= mod) return 0;
while (int(dat.size()) <= n) {
int k = dat.size();
dat.emplace_back(dat[k - 1] * mint(k));
}
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {1, 1};
assert(-1 <= n && n < mod);
if (n == -1) return mint(0);
while (int(dat.size()) <= n) {
int k = dat.size();
dat.emplace_back(dat[k - 1] * inv<mint>(k));
}
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
static vvc<mint> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if (dense) return C_dense<mint>(n, k);
if (!large) return fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) { x *= mint(n - i); }
x *= fact_inv<mint>(k);
return x;
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d] (1-x) ^ {-n} の計算
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
using amint = ArbitraryModInt;
#line 2 "/home/maspy/compro/library/random/base.hpp"
u64 RNG_64() {
static uint64_t x_
= uint64_t(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 2 "/home/maspy/compro/library/nt/primetest.hpp"
struct m64 {
using i64 = int64_t;
using u64 = uint64_t;
using u128 = __uint128_t;
inline static u64 m, r, n2; // r * m = -1 (mod 1<<64), n2 = 1<<128 (mod m)
static void set_mod(u64 m) {
assert((m & 1) == 1);
m64::m = m;
n2 = -u128(m) % m;
r = m;
FOR(_, 5) r *= 2 - m * r;
r = -r;
assert(r * m == -1ull);
}
static u64 reduce(u128 b) { return (b + u128(u64(b) * r) * m) >> 64; }
u64 x;
m64() : x(0) {}
m64(u64 x) : x(reduce(u128(x) * n2)){};
u64 val() const {
u64 y = reduce(x);
return y >= m ? y - m : y;
}
m64 &operator+=(m64 y) {
x += y.x - (m << 1);
x = (i64(x) < 0 ? x + (m << 1) : x);
return *this;
}
m64 &operator-=(m64 y) {
x -= y.x;
x = (i64(x) < 0 ? x + (m << 1) : x);
return *this;
}
m64 &operator*=(m64 y) {
x = reduce(u128(x) * y.x);
return *this;
}
m64 operator+(m64 y) const { return m64(*this) += y; }
m64 operator-(m64 y) const { return m64(*this) -= y; }
m64 operator*(m64 y) const { return m64(*this) *= y; }
bool operator==(m64 y) const {
return (x >= m ? x - m : x) == (y.x >= m ? y.x - m : y.x);
}
bool operator!=(m64 y) const { return not operator==(y); }
m64 pow(u64 n) const {
m64 y = 1, z = *this;
for (; n; n >>= 1, z *= z)
if (n & 1) y *= z;
return y;
}
};
bool primetest(const uint64_t x) {
using u64 = uint64_t;
if (x == 2 or x == 3 or x == 5 or x == 7) return true;
if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false;
if (x < 121) return x > 1;
const u64 d = (x - 1) >> __builtin_ctzll(x - 1);
m64::set_mod(x);
const m64 one(1), minus_one(x - 1);
auto ok = [&](u64 a) {
auto y = m64(a).pow(d);
u64 t = d;
while (y != one and y != minus_one and t != x - 1) y *= y, t <<= 1;
if (y != minus_one and t % 2 == 0) return false;
return true;
};
if (x < (1ull << 32)) {
for (u64 a: {2, 7, 61})
if (not ok(a)) return false;
} else {
for (u64 a: {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
if (x <= a) return true;
if (not ok(a)) return false;
}
}
return true;
}
#line 2 "/home/maspy/compro/library/mod/fast_div.hpp"
struct fast_div {
// Min25 https://judge.yosupo.jp/submission/46090
// 同じ定数で何度も除算するときの高速化に使える
using i64 = long long;
using u64 = unsigned long long;
using u128 = __uint128_t;
constexpr fast_div() : m(), s(), x() {}
constexpr fast_div(int n)
: m(n), s(std::__lg(n - 1)), x(((u128(1) << (s + 64)) + n - 1) / n) {}
constexpr friend u64 operator/(u64 n, const fast_div& d) {
return (u128(n) * d.x >> d.s) >> 64;
}
constexpr friend int operator%(u64 n, const fast_div& d) {
return n - n / d * d.m;
}
constexpr std::pair<i64, int> divmod(u64 n) const {
u64 q = n / *this;
return {q, n - q * m};
}
int m;
int s;
u64 x;
};
#line 3 "/home/maspy/compro/library/mod/mod_pow.hpp"
// int
ll mod_pow(ll a, ll n, int mod){
fast_div fd(mod);
a = a % fd;
ll p = a;
ll v = 1;
while(n){
if(n & 1) v = v * p % fd;
p = p * p % fd;
n >>= 1;
}
return v;
}
ll mod_pow_long(ll a, ll n, ll mod){
a %= mod;
ll p = a;
ll v = 1;
while(n){
if(n & 1) v = i128(v) * p % mod;
p = i128(p) * p % mod;
n >>= 1;
}
return v;
}
#line 7 "main.cpp"
using M1 = modint998;
using M2 = modint107;
void solve() {
LL(K);
VEC(pi, PE, K);
M1 N1 = 1;
M2 N2 = 1;
for (auto&& [p, e]: PE) {
N1 *= M1(p).pow(e);
N2 *= M2(p).pow(e);
}
ll p = PE.back().fi;
if (PE.back().se != 1) return print(-1, -1);
auto check = [&](ll p, ll a, ll b) -> bool {
FOR(5) {
int mod;
while (1) {
mod = RNG(1'000'000'00, 1'000'000'000);
if (!primetest(mod)) continue;
break;
}
ll xp = 1, xa = 1, xb = 1, xN = 1;
for (auto&& [p, e]: PE) { xN = xN * mod_pow(p, e, mod) % mod; }
ll f = 1;
FOR(k, p + 1) {
if (k == p) xp = f;
if (k == a) xa = f;
if (k == b) xb = f;
f = f * (k + 1) % mod;
}
if (xN * xa % mod * xb % mod != xp) return 0;
}
return 1;
};
FOR(a, p + 1) {
ll b = p - a;
if (fact<M1>(a) * fact<M1>(b) * N1 != fact<M1>(p)) continue;
if (fact<M2>(a) * fact<M2>(b) * N2 != fact<M2>(p)) continue;
if (check(p, a, b)) { return print(p, a); }
}
print(-1, -1);
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}