結果
| 問題 |
No.8038 フィボナッチ数列の周期
|
| ユーザー |
 tko919
|
| 提出日時 | 2025-05-03 09:31:04 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 104 ms / 3,000 ms |
| コード長 | 27,077 bytes |
| コンパイル時間 | 3,773 ms |
| コンパイル使用メモリ | 257,948 KB |
| 実行使用メモリ | 7,844 KB |
| 最終ジャッジ日時 | 2025-05-03 09:31:10 |
| 合計ジャッジ時間 | 6,205 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 25 |
ソースコード
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template <typename T, typename S = T> S SUM(const vector<T> &a) {
return accumulate(ALL(a), S(0));
}
template <typename S, typename T = S> S POW(S a, T b) {
S ret = 1, base = a;
for (;;) {
if (b & 1)
ret *= base;
b >>= 1;
if (b == 0)
break;
base *= base;
}
return ret;
}
template <typename T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return 1;
}
return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return 1;
}
return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << "P(" << p.first << ", " << p.second << ")";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
os << "{";
for (int i = 0; i < vec.size(); i++) {
os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
}
os << "}";
return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
os << "{";
for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
os << "(" << itr->first << ", " << itr->second << ")";
itr++;
if (itr != map_var.end())
os << ", ";
itr--;
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
os << "{";
for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
os << *itr;
++itr;
if (itr != set_var.end())
os << ", ";
itr--;
}
os << "}";
return os;
}
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
for (; a[i] != ',' && a[i] != '\0'; i++)
cerr << a[i];
cerr << ":" << b << " ";
_show(i + 1, a, c...);
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memmove(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ)
ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir)
load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir)
load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir)
load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T> void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T> void rd_integer(T &x) {
if (pil + 100 > pir)
load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') {
minus = 1, c = ibuf[pil++];
}
}
x = 0;
while ('0' <= c) {
x = x * 10 + (c & 15), c = ibuf[pil++];
}
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus)
x = -x;
}
}
void rd(int &x) {
rd_integer(x);
}
void rd(ll &x) {
rd_integer(x);
}
void rd(i128 &x) {
rd_integer(x);
}
void rd(uint &x) {
rd_integer(x);
}
void rd(ull &x) {
rd_integer(x);
}
void rd(u128 &x) {
rd_integer(x);
}
void rd(double &x) {
rd_real(x);
}
void rd(long double &x) {
rd_real(x);
}
template <class T, class U> void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T> void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T> void rd(array<T, N> &x) {
for (auto &d : x)
rd(d);
}
template <class T> void rd(vector<T> &x) {
for (auto &d : x)
rd(d);
}
void read() {}
template <class H, class... T> void read(H &h, T &...t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ)
flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c : s)
wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++)
wt(s[i]);
}
template <typename T> void wt_integer(T x) {
if (por > SZ - 100)
flush();
if (x < 0) {
obuf[por++] = '-', x = -x;
}
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T> void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) {
wt_integer(x);
}
void wt(ll x) {
wt_integer(x);
}
void wt(i128 x) {
wt_integer(x);
}
void wt(uint x) {
wt_integer(x);
}
void wt(ull x) {
wt_integer(x);
}
void wt(u128 x) {
wt_integer(x);
}
void wt(double x) {
wt_real(x);
}
void wt(long double x) {
wt_real(x);
}
template <class T, class U> void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) {
wt(' ');
}
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T> void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i)
wt(' ');
wt(val[i]);
}
}
template <class T> void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i)
wt(' ');
wt(val[i]);
}
}
void print() {
wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
wt(head);
if (sizeof...(Tail))
wt(' ');
print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
flush();
}
} // namespace fastio
using fastio::flush;
using fastio::print;
using fastio::read;
inline void first(bool i = true) {
print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
print(i ? "Alice" : "Bob");
}
inline void Takahashi(bool i = true) {
print(i ? "Takahashi" : "Aoki");
}
inline void yes(bool i = true) {
print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
print(i ? "Yes" : "No");
}
inline void No() {
print("No");
}
inline void YES(bool i = true) {
print(i ? "YES" : "NO");
}
inline void NO() {
print("NO");
}
inline void Yay(bool i = true) {
print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
print(i ? "POSSIBLE" : "IMPOSSIBLE");
}
/**
* @brief Fast IO
*/
#line 2 "library/Utility/random.hpp"
namespace Random {
mt19937_64 randgen(chrono::steady_clock::now().time_since_epoch().count());
using u64 = unsigned long long;
u64 get() {
return randgen();
}
template <typename T> T get(T L) { // [0,L]
return get() % (L + 1);
}
template <typename T> T get(T L, T R) { // [L,R]
return get(R - L) + L;
}
double uniform() {
return double(get(1000000000)) / 1000000000;
}
string str(int n) {
string ret;
rep(i, 0, n) ret += get('a', 'z');
return ret;
}
template <typename Iter> void shuffle(Iter first, Iter last) {
if (first == last)
return;
int len = 1;
for (auto it = first + 1; it != last; it++) {
len++;
int j = get(0, len - 1);
if (j != len - 1)
iter_swap(it, first + j);
}
}
template <typename T> vector<T> select(int n, T L, T R) { // [L,R]
if (n * 2 >= R - L + 1) {
vector<T> ret(R - L + 1);
iota(ALL(ret), L);
shuffle(ALL(ret));
ret.resize(n);
return ret;
} else {
unordered_set<T> used;
vector<T> ret;
while (SZ(used) < n) {
T x = get(L, R);
if (!used.count(x)) {
used.insert(x);
ret.push_back(x);
}
}
return ret;
}
}
void relabel(int n, vector<pair<int, int>> &es) {
shuffle(ALL(es));
vector<int> ord(n);
iota(ALL(ord), 0);
shuffle(ALL(ord));
for (auto &[u, v] : es)
u = ord[u], v = ord[v];
}
template <bool directed, bool simple>
vector<pair<int, int>> genGraph(int n, int m) {
vector<pair<int, int>> cand, es;
rep(u, 0, n) rep(v, 0, n) {
if (simple and u == v)
continue;
if (!directed and u > v)
continue;
cand.push_back({u, v});
}
if (m == -1)
m = get(SZ(cand));
chmin(m, SZ(cand));
vector<int> ord;
if (simple)
ord = select(m, 0, SZ(cand) - 1);
else {
rep(_, 0, m) ord.push_back(get(SZ(cand) - 1));
}
for (auto &i : ord)
es.push_back(cand[i]);
relabel(n, es);
return es;
}
vector<pair<int, int>> genTree(int n) {
vector<pair<int, int>> es;
rep(i, 1, n) es.push_back({get(i - 1), i});
relabel(n, es);
return es;
}
}; // namespace Random
/**
* @brief Random
*/
#line 4 "sol.cpp"
#line 2 "library/Math/fastdiv.hpp"
struct FastDiv {
using u64 = uint64_t;
using u128 = __uint128_t;
constexpr FastDiv() : m(), s(), x() {}
constexpr FastDiv(int _m)
: m(_m), s(__lg(m - 1)), x(((u128(1) << (s + 64)) + m - 1) / m) {}
constexpr int get() {
return m;
}
constexpr friend u64 operator/(u64 n, const FastDiv &d) {
return (u128(n) * d.x >> d.s) >> 64;
}
constexpr friend int operator%(u64 n, const FastDiv &d) {
return n - n / d * d.m;
}
constexpr pair<u64, int> divmod(u64 n) const {
u64 q = n / (*this);
return {q, n - q * m};
}
int m, s;
u64 x;
};
struct FastDiv64 {
using u64 = uint64_t;
using u128 = __uint128_t;
u128 mod, mh, ml;
explicit FastDiv64(u64 mod = 1) : mod(mod) {
u128 m = u128(-1) / mod;
if (m * mod + mod == u128(0))
++m;
mh = m >> 64;
ml = m & u64(-1);
}
u64 umod() const {
return mod;
}
u64 modulo(u128 x) {
u128 z = (x & u64(-1)) * ml;
z = (x & u64(-1)) * mh + (x >> 64) * ml + (z >> 64);
z = (x >> 64) * mh + (z >> 64);
x -= z * mod;
return x < mod ? x : x - mod;
}
u64 mul(u64 a, u64 b) {
return modulo(u128(a) * b);
}
};
/**
* @brief Fast Division
*/
#line 3 "library/Math/dynamic.hpp"
struct Fp {
using u64 = uint64_t;
uint v;
static uint get_mod() {
return _getmod();
}
static void set_mod(uint _m) {
bar = FastDiv(_m);
}
Fp inv() const {
int tmp, a = v, b = get_mod(), x = 1, y = 0;
while (b) {
tmp = a / b, a -= tmp * b;
swap(a, b);
x -= tmp * y;
swap(x, y);
}
if (x < 0) {
x += get_mod();
}
return x;
}
Fp() : v(0) {}
Fp(ll x) {
v = x % get_mod();
if (v < 0)
v += get_mod();
}
Fp operator-() const {
return Fp() - *this;
}
Fp pow(ll t) {
assert(t >= 0);
Fp res = 1, b = *this;
while (t) {
if (t & 1)
res *= b;
b *= b;
t >>= 1;
}
return res;
}
Fp &operator+=(const Fp &x) {
v += x.v;
if (v >= get_mod())
v -= get_mod();
return *this;
}
Fp &operator-=(const Fp &x) {
v += get_mod() - x.v;
if (v >= get_mod())
v -= get_mod();
return *this;
}
Fp &operator*=(const Fp &x) {
v = (u64(v) * x.v) % bar;
return *this;
}
Fp &operator/=(const Fp &x) {
(*this) *= x.inv();
return *this;
}
Fp operator+(const Fp &x) const {
return Fp(*this) += x;
}
Fp operator-(const Fp &x) const {
return Fp(*this) -= x;
}
Fp operator*(const Fp &x) const {
return Fp(*this) *= x;
}
Fp operator/(const Fp &x) const {
return Fp(*this) /= x;
}
bool operator==(const Fp &x) const {
return v == x.v;
}
bool operator!=(const Fp &x) const {
return v != x.v;
}
friend istream &operator>>(istream &is, Fp &x) {
return is >> x.v;
}
friend ostream &operator<<(ostream &os, const Fp &x) {
return os << x.v;
}
private:
static FastDiv bar;
static uint _getmod() {
return bar.get();
}
};
FastDiv Fp::bar(998244353);
void rd(Fp &x) {
fastio::rd(x.v);
}
void wt(Fp x) {
fastio::wt(x.v);
}
/**
* @brief Dynamic Modint
*/
#line 2 "library/Math/matrix.hpp"
template <class T> struct Matrix {
int h, w;
vector<vector<T>> val;
T det;
Matrix() {}
Matrix(int n) : h(n), w(n), val(vector<vector<T>>(n, vector<T>(n))) {}
Matrix(int n, int m)
: h(n), w(m), val(vector<vector<T>>(n, vector<T>(m))) {}
vector<T> &operator[](const int i) {
return val[i];
}
Matrix &operator+=(const Matrix &m) {
assert(h == m.h and w == m.w);
rep(i, 0, h) rep(j, 0, w) val[i][j] += m.val[i][j];
return *this;
}
Matrix &operator-=(const Matrix &m) {
assert(h == m.h and w == m.w);
rep(i, 0, h) rep(j, 0, w) val[i][j] -= m.val[i][j];
return *this;
}
Matrix &operator*=(const Matrix &m) {
assert(w == m.h);
Matrix<T> res(h, m.w);
rep(i, 0, h) rep(j, 0, m.w) rep(k, 0, w) res.val[i][j] +=
val[i][k] * m.val[k][j];
*this = res;
return *this;
}
Matrix operator+(const Matrix &m) const {
return Matrix(*this) += m;
}
Matrix operator-(const Matrix &m) const {
return Matrix(*this) -= m;
}
Matrix operator*(const Matrix &m) const {
return Matrix(*this) *= m;
}
Matrix pow(ll k) {
Matrix<T> res(h, h), c = *this;
rep(i, 0, h) res.val[i][i] = 1;
while (k) {
if (k & 1)
res *= c;
c *= c;
k >>= 1;
}
return res;
}
vector<int> gauss(int c = -1) {
det = 1;
if (val.empty())
return {};
if (c == -1)
c = w;
int cur = 0;
vector<int> res;
rep(i, 0, c) {
if (cur == h)
break;
rep(j, cur, h) if (val[j][i] != 0) {
swap(val[cur], val[j]);
if (cur != j)
det *= -1;
break;
}
det *= val[cur][i];
if (val[cur][i] == 0)
continue;
rep(j, 0, h) if (j != cur) {
T z = val[j][i] / val[cur][i];
rep(k, i, w) val[j][k] -= val[cur][k] * z;
}
res.push_back(i);
cur++;
}
return res;
}
Matrix inv() {
assert(h == w);
Matrix base(h, h * 2), res(h, h);
rep(i, 0, h) rep(j, 0, h) base[i][j] = val[i][j];
rep(i, 0, h) base[i][h + i] = 1;
base.gauss(h);
det = base.det;
rep(i, 0, h) rep(j, 0, h) res[i][j] = base[i][h + j] / base[i][i];
return res;
}
bool operator==(const Matrix &m) {
assert(h == m.h and w == m.w);
rep(i, 0, h) rep(j, 0, w) if (val[i][j] != m.val[i][j]) return false;
return true;
}
bool operator!=(const Matrix &m) {
assert(h == m.h and w == m.w);
rep(i, 0, h) rep(j, 0, w) if (val[i][j] == m.val[i][j]) return false;
return true;
}
friend istream &operator>>(istream &is, Matrix &m) {
rep(i, 0, m.h) rep(j, 0, m.w) is >> m[i][j];
return is;
}
friend ostream &operator<<(ostream &os, Matrix &m) {
rep(i, 0, m.h) {
rep(j, 0, m.w) os << m[i][j]
<< (j == m.w - 1 and i != m.h - 1 ? '\n' : ' ');
}
return os;
}
};
/**
* @brief Matrix
*/
#line 2 "library/Math/miller.hpp"
struct m64 {
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;
rep(_,0,5) 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);
}
static u64 get_mod() { return mod; }
u64 a;
m64() : a(0) {}
m64(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;
}
u64 get() const {
u64 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
m64 &operator*=(const m64 &b) {
a = reduce(u128(a) * b.a);
return *this;
}
m64 operator*(const m64 &b) const { return m64(*this) *= b; }
bool operator==(const m64 &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(const m64 &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
m64 pow(u128 n) const {
m64 ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
};
typename m64::u64 m64::mod, m64::r, m64::n2;
bool Miller(ll n){
if(n<2 or (n&1)==0)return (n==2);
m64::set_mod(n);
ll d=n-1; while((d&1)==0)d>>=1;
vector<ll> seeds;
if(n<(1<<30))seeds={2, 7, 61};
else seeds={2, 325, 9375, 28178, 450775, 9780504};
for(auto& x:seeds){
if(n<=x)break;
ll t=d;
m64 y=m64(x).pow(t);
while(t!=n-1 and y!=1 and y!=n-1){
y*=y;
t<<=1;
}
if(y!=n-1 and (t&1)==0)return 0;
} return 1;
}
/**
* @brief Miller-Rabin
*/
#line 4 "library/Math/pollard.hpp"
vector<ll> Pollard(ll n) {
if (n <= 1)
return {};
if (Miller(n))
return {n};
if ((n & 1) == 0) {
vector<ll> v = Pollard(n >> 1);
v.push_back(2);
return v;
}
for (ll x = 2, y = 2, d;;) {
ll c = Random::get(2LL, n - 1);
do {
x = (__int128_t(x) * x + c) % n;
y = (__int128_t(y) * y + c) % n;
y = (__int128_t(y) * y + c) % n;
d = __gcd(x - y + n, n);
} while (d == 1);
if (d < n) {
vector<ll> lb = Pollard(d), rb = Pollard(n / d);
lb.insert(lb.end(), ALL(rb));
return lb;
}
}
}
vector<pair<ll, int>> Pollard2(ll n) {
auto ps = Pollard(n);
sort(ALL(ps));
using P = pair<ll, int>;
vector<P> pes;
for (auto &p : ps) {
if (pes.empty() or pes.back().first != p) {
pes.push_back({p, 1});
} else {
pes.back().second++;
}
}
return pes;
}
vector<ll> EnumDivisors(ll n) {
auto pes = Pollard2(n);
vector<ll> ret;
auto rec = [&](auto &rec, int id, ll d) -> void {
if (id == SZ(pes)) {
ret.push_back(d);
return;
}
rec(rec, id + 1, d);
rep(e, 0, pes[id].second) {
d *= pes[id].first;
rec(rec, id + 1, d);
}
};
rec(rec, 0, 1);
sort(ALL(ret));
return ret;
}
/**
* @brief Pollard-Rho
*/
#line 8 "sol.cpp"
int Pisano(int p) {
if (p == 2)
return 3;
if (p == 5)
return 20;
vector<ll> cand;
if (p % 5 == 1 or p % 5 == 4)
cand = EnumDivisors(p - 1);
else
cand = EnumDivisors(p * 2 + 2);
auto check = [&](int d, int p) -> bool {
Fp::set_mod(p);
Matrix<Fp> mat(2, 2);
mat[0][1] = mat[1][0] = mat[1][1] = 1;
mat = mat.pow(d);
return mat[0][1] == 0 and mat[1][1] == 1;
};
for (auto &d : cand)
if (check(d, p)) {
return d;
}
assert(0);
}
#line 2 "library/Math/modint.hpp"
template <unsigned mod = 1000000007> struct fp {
unsigned v;
static constexpr int get_mod() {
return mod;
}
constexpr unsigned inv() const {
assert(v != 0);
int x = v, y = mod, p = 1, q = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, p -= t * q;
tmp = x, x = y, y = tmp;
tmp = p, p = q, q = tmp;
}
if (p < 0)
p += mod;
return p;
}
constexpr fp(ll x = 0) : v(x >= 0 ? x % mod : (mod - (-x) % mod) % mod) {}
fp operator-() const {
return fp() - *this;
}
fp pow(ull t) {
fp res = 1, b = *this;
while (t) {
if (t & 1)
res *= b;
b *= b;
t >>= 1;
}
return res;
}
fp &operator+=(const fp &x) {
if ((v += x.v) >= mod)
v -= mod;
return *this;
}
fp &operator-=(const fp &x) {
if ((v += mod - x.v) >= mod)
v -= mod;
return *this;
}
fp &operator*=(const fp &x) {
v = ull(v) * x.v % mod;
return *this;
}
fp &operator/=(const fp &x) {
v = ull(v) * x.inv() % mod;
return *this;
}
fp operator+(const fp &x) const {
return fp(*this) += x;
}
fp operator-(const fp &x) const {
return fp(*this) -= x;
}
fp operator*(const fp &x) const {
return fp(*this) *= x;
}
fp operator/(const fp &x) const {
return fp(*this) /= x;
}
bool operator==(const fp &x) const {
return v == x.v;
}
bool operator!=(const fp &x) const {
return v != x.v;
}
friend istream &operator>>(istream &is, fp &x) {
return is >> x.v;
}
friend ostream &operator<<(ostream &os, const fp &x) {
return os << x.v;
}
};
template <unsigned mod> void rd(fp<mod> &x) {
fastio::rd(x.v);
}
template <unsigned mod> void wt(fp<mod> x) {
fastio::wt(x.v);
}
/**
* @brief Modint
*/
#line 2 "library/Math/comb.hpp"
template <typename T> T Inv(ll n) {
static int md;
static vector<T> buf({0, 1});
if (md != T::get_mod()) {
md = T::get_mod();
buf = vector<T>({0, 1});
}
assert(n > 0);
n %= md;
while (SZ(buf) <= n) {
int k = SZ(buf), q = (md + k - 1) / k;
buf.push_back(buf[k * q - md] * q);
}
return buf[n];
}
template <typename T> T Fact(ll n, bool inv = 0) {
static int md;
static vector<T> buf({1, 1}), ibuf({1, 1});
if (md != T::get_mod()) {
md = T::get_mod();
buf = ibuf = vector<T>({1, 1});
}
assert(n >= 0 and n < md);
while (SZ(buf) <= n) {
buf.push_back(buf.back() * SZ(buf));
ibuf.push_back(ibuf.back() * Inv<T>(SZ(ibuf)));
}
return inv ? ibuf[n] : buf[n];
}
template <typename T> T nPr(int n, int r, bool inv = 0) {
if (n < 0 || n < r || r < 0)
return 0;
return Fact<T>(n, inv) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nCr(int n, int r, bool inv = 0) {
if (n < 0 || n < r || r < 0)
return 0;
return Fact<T>(n, inv) * Fact<T>(r, inv ^ 1) * Fact<T>(n - r, inv ^ 1);
}
// sum = n, r tuples
template <typename T> T nHr(int n, int r, bool inv = 0) {
return nCr<T>(n + r - 1, r - 1, inv);
}
// sum = n, a nonzero tuples and b tuples
template <typename T> T choose(int n, int a, int b) {
if (n == 0)
return !a;
return nCr<T>(n + b - 1, a + b - 1);
}
/**
* @brief Combination
*/
#line 35 "sol.cpp"
using X = fp<>;
int main() {
int n;
read(n);
vector<int> p(n), k(n);
rep(i, 0, n) read(p[i], k[i]);
map<int, int> L;
rep(i, 0, n) {
int base = Pisano(p[i]);
show(p[i], base);
auto pes = Pollard2(base);
bool ch = 0;
for (auto &[P, e] : pes) {
if (P == p[i]) {
e += k[i] - 1;
ch = 1;
}
chmax(L[P], e);
}
if (!ch)
chmax(L[p[i]], k[i] - 1);
}
X ret = 1;
for (auto &[p, e] : L)
ret *= X(p).pow(e);
print(ret);
return 0;
}