#include #define ll long long #define INF 1000000005 #define MOD 1000000007 #define EPS 1e-10 #define rep(i,n) for(int i=0;i<(int)(n);++i) #define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i) #define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i) #define each(a,b) for(auto& (a): (b)) #define all(v) (v).begin(),(v).end() #define len(v) (int)(v).size() #define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end()) #define cmx(x,y) x=max(x,y) #define cmn(x,y) x=min(x,y) #define fi first #define se second #define pb push_back #define show(x) cout<<#x<<" = "<<(x)<auto&operator<<(ostream&o,pairp){return o<<"{"<auto&operator<<(ostream&o,sets){for(auto&e:s)o< auto&operator<<(ostream&o,priority_queueq){while(!q.empty())o<auto&operator<<(ostream&o,map&m){for(auto&e:m)o<auto&operator<<(ostream&o,vectorv){for(auto&e:v)o<void ashow(T t,A...a){cout< struct TRI{S fi;T se;U th;TRI(){}TRI(S f,T s,U t):fi(f),se(s),th(t){} bool operator<(const TRI&_)const{return(fi==_.fi)?((se==_.se)?(th<_.th):(se<_.se)):(fi<_.fi);}}; template auto&operator<<(ostream&o,TRI&t){return o<<"{"< P; typedef pair pll; typedef TRI tri; typedef vector vi; typedef vector vl; typedef vector vvi; typedef vector vvl; typedef vector

vp; typedef vector vd; typedef vector vs; const int MAX_N = 32005; template class UnorderedMapIterator; template, bool DOWNSIZE = false> class UnorderedMap { private: using iterator = UnorderedMapIterator<_Key, _Tp, _Hash, DOWNSIZE>; using value_type = _Tp; using data_type = pair<_Key, _Tp>; using aligned_pointer = typename aligned_storage::type; friend UnorderedMapIterator<_Key, _Tp, _Hash, DOWNSIZE>; struct bucket { _Key _key; short int _dist; bool _last, _end; aligned_pointer _value_ptr; bucket() noexcept : _dist(-1), _last(false), _end(false){} bucket& operator=(const bucket& another) noexcept { _key = another._key, _dist = another._dist, _last = another._last, _end = another._end; if(!another.empty()){ new(&_value_ptr) value_type(*reinterpret_cast(&another._value_ptr)); } return *this; } ~bucket(){ if(!empty()) _delete(); } inline void clear() noexcept { _dist = -1; } inline void _delete(){ _dist = -1, value_ptr()->~value_type(); } inline bool empty() const noexcept { return (_dist == -1); } inline value_type& value() noexcept { return *reinterpret_cast(&_value_ptr); } inline value_type* value_ptr() noexcept { return reinterpret_cast(&_value_ptr); } inline void new_value(value_type&& value){ new(&_value_ptr) value_type(move(value)); } }; inline static unsigned int ceilpow2(unsigned int u) noexcept { --u, u |= u >> 1, u |= u >> 2, u |= u >> 4, u |= u >> 8; return (u | (u >> 16)) + 1; } inline static bucket *increment(bucket *cur) noexcept { for(++cur; !cur->_end; ++cur){ if(!cur->empty()) break; } return cur; } inline bucket *next_bucket(bucket *cur) const noexcept { return cur->_last ? _buckets : cur + 1; } inline unsigned int make_hash(const _Key& key) const noexcept { return _Hash()(key); } inline float load_rate() const noexcept { return (float)_data_count / _bucket_count; } bucket *insert(bucket *cur, _Key&& key, short int dist, value_type&& value){ bucket *ret = cur; bool flag = false; while(true){ if(cur->empty()){ cur->_key = move(key), cur->_dist = dist, cur->new_value(move(value)); if(!flag) ret = cur, flag = true; break; }else if(dist > cur->_dist){ swap(key, cur->_key), swap(dist, cur->_dist), swap(value, cur->value()); if(!flag) ret = cur, flag = true; } ++dist; cur = next_bucket(cur); } return ret; } template bucket *_find(Key&& key, bool push = false){ unsigned int hash = make_hash(key); bucket *cur = _buckets + (hash & _mask); short int dist = 0; while(dist <= cur->_dist){ if(key == cur->_key) return cur; ++dist, cur = next_bucket(cur); } if(!push) return _buckets + _bucket_count; ++_data_count; if(rehash_check()){ cur = _buckets + (hash & _mask), dist = 0; } value_type new_value = value_type(); _Key new_key = forward(key); return insert(cur, move(new_key), dist, move(new_value)); } template bucket *find_insert(Data&& data){ const _Key& key = data.first; unsigned int hash = make_hash(key); bucket *cur = _buckets + (hash & _mask); short int dist = 0; while(dist <= cur->_dist){ if(key == cur->_key) return cur; ++dist, cur = next_bucket(cur); } ++_data_count; if(rehash_check()){ cur = _buckets + (hash & _mask), dist = 0; } data_type new_data = forward(data); return insert(cur, move(new_data.first), dist, move(new_data.second)); } template bucket *emplace(Args&&... args){ return find_insert(data_type(forward(args)...)); } bucket *backward_shift(bucket *cur, bool next_ret){ bucket *next = next_bucket(cur), *ret = cur; if(next->_dist < 1) return next_ret ? increment(cur) : cur; do { cur->_key = next->_key, cur->_dist = next->_dist - 1; cur->new_value(move(next->value())); cur = next, next = next_bucket(cur); }while(next->_dist >= 1); cur->clear(); return ret; } bucket *erase_impl(bucket *cur, bool next_ret){ assert(static_cast(cur - _buckets) != _bucket_count); cur->_delete(); --_data_count; return backward_shift(cur, next_ret); } bucket *erase_itr(bucket *cur, bool next_ret = true){ const _Key key = cur->_key; return erase_impl(rehash_check() ? _find(key) : cur, next_ret); } bucket *erase_key(const _Key& key, bool next_ret = true){ rehash_check(); return erase_impl(_find(key), next_ret); } bool rehash_check(){ if(load_rate() >= MAX_LOAD_RATE){ rehash(_bucket_count * 2u); return true; }else if(DOWNSIZE){ if(load_rate() <= MIN_LOAD_RATE && _bucket_count >= DOWNSIZE_THRESHOLD){ rehash(_bucket_count / 2u); return true; } } return false; } void move_data(bucket *cur){ insert(_buckets + (make_hash(cur->_key) & _mask), move(cur->_key), 0, move(cur->value())); } void rehash(unsigned int new_bucket_count){ UnorderedMap new_unordered_map(new_bucket_count); new_unordered_map._data_count = _data_count; for(bucket *cur = _buckets; !cur->_end; ++cur){ if(!cur->empty()){ new_unordered_map.move_data(cur); } } swap(*this, new_unordered_map); } friend void swap(UnorderedMap& ump1, UnorderedMap& ump2){ swap(ump1._bucket_count, ump2._bucket_count); swap(ump1._mask, ump2._mask); swap(ump1._data_count, ump2._data_count); swap(ump1._buckets, ump2._buckets); } private: unsigned int _bucket_count, _mask, _data_count; bucket *_buckets; public: const float MAX_LOAD_RATE = 0.5f; const float MIN_LOAD_RATE = 0.1f; const unsigned int DOWNSIZE_THRESHOLD = 16u; UnorderedMap(unsigned int bucket_size = 1u) : _bucket_count(ceilpow2(max(bucket_size, 1u))), _mask(_bucket_count - 1), _data_count(0u), _buckets(new bucket[_bucket_count + 1]){ _buckets[_bucket_count - 1]._last = true, _buckets[_bucket_count]._end = true; } UnorderedMap(const UnorderedMap& another) : _bucket_count(another._bucket_count), _mask(another._mask), _data_count(another._data_count){ _buckets = new bucket[_bucket_count + 1u]; for(unsigned int i = 0u; i <= _bucket_count; ++i){ _buckets[i] = another._buckets[i]; } } UnorderedMap(UnorderedMap&& another) : _bucket_count(move(another._bucket_count)), _mask(move(another._mask)), _data_count(move(another._data_count)), _buckets(another._buckets){ another._buckets = nullptr; } UnorderedMap& operator=(const UnorderedMap& another){ delete[] _buckets; _bucket_count = another._bucket_count; _mask = another._mask; _data_count = another._data_count; _buckets = new bucket[_bucket_count + 1u]; for(unsigned int i = 0u; i <= _bucket_count; ++i){ _buckets[i] = another._buckets[i]; } return *this; } UnorderedMap& operator=(UnorderedMap&& another){ delete[] _buckets; _bucket_count = move(another._bucket_count); _mask = move(another._mask); _data_count = move(another._data_count); _buckets = another._buckets; another._buckets = nullptr; return *this; } ~UnorderedMap(){ delete[] _buckets; } friend ostream& operator<< (ostream& os, UnorderedMap& ump) noexcept { for(auto val : ump) os << '{' << val.first << ',' << val.second << "} "; return os; } _Tp& operator[](const _Key& key){ return _find(key, true)->value(); } _Tp& operator[](_Key&& key){ return _find(move(key), true)->value(); } const _Tp& at(const _Key& key){ bucket *res = _find(key); if(res == _buckets + _bucket_count) __throw_out_of_range(__N("Unordered_Map::at")); return res->value(); } void clear(){ UnorderedMap new_unordered_map(1u); swap(*this, new_unordered_map); } size_t size() const noexcept { return _data_count; } size_t bucket_count() const noexcept { return _bucket_count; } bool empty() const noexcept { return (_data_count == 0); } iterator begin() noexcept { return _buckets->empty() ? iterator(increment(_buckets)) : iterator(_buckets); } iterator end() noexcept { return iterator(_buckets + _bucket_count); } iterator find(const _Key& key){ return iterator(_find(key)); } iterator insert(const data_type& data){ return iterator(find_insert(data)); } iterator insert(data_type&& data){ return iterator(find_insert(move(data))); } template iterator emplace(Args&&... args){ return iterator(_emplace(forward(args)...)); } iterator erase(const _Key& key){ return iterator(erase_key(key)); } iterator erase(const iterator& itr){ return iterator(erase_itr(itr.bucket_ptr)); } void simple_erase(const _Key& key){ erase_key(key, false); } void simple_erase(const iterator& itr){ erase_itr(itr.bucket_ptr, false); } // DEBUG 用 short int maximum_distance() const noexcept { short int ret = -1; for(bucket *cur = _buckets; !cur->_end; ++cur){ ret = max(ret, cur->_dist); } return ret; } }; template class UnorderedMapIterator { private: friend UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>; typename UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::bucket *bucket_ptr; using iterator_category = forward_iterator_tag; using value_type = pair; using difference_type = ptrdiff_t; using reference = pair; private: UnorderedMapIterator(typename UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::bucket *_bucket_ptr) noexcept : bucket_ptr(_bucket_ptr){} public: UnorderedMapIterator() noexcept : bucket_ptr(){} UnorderedMapIterator(const UnorderedMapIterator& itr) noexcept : bucket_ptr(itr.bucket_ptr){} UnorderedMapIterator& operator=(const UnorderedMapIterator& itr) & noexcept { return bucket_ptr = itr.bucket_ptr, *this; } UnorderedMapIterator& operator=(const UnorderedMapIterator&& itr) & noexcept { return bucket_ptr = itr.bucket_ptr, *this; } reference operator*() const noexcept { return {bucket_ptr->_key, bucket_ptr->value()}; } UnorderedMapIterator& operator++() noexcept { return bucket_ptr = UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::increment(bucket_ptr), *this; } UnorderedMapIterator operator++(int) const noexcept { return UnorderedMapIterator(UnorderedMap<_Key, _Tp, _Hash, DOWNSIZE>::increment(this->bucket_ptr)); } bool operator==(const UnorderedMapIterator& itr) const noexcept { return !(*this != itr); }; bool operator!=(const UnorderedMapIterator& itr) const noexcept { return bucket_ptr != itr.bucket_ptr; } }; template T mod_add(const T a, const T b, const T mod){ return (a + b) % mod; } template T mod_mul(const T a, const T b, const T mod){ return a * b % mod; } template T mod_pow(T a, T b, const T mod){ T res = 1; while(b){ if(b & 1){ res = mod_mul(res, a, mod); } a = mod_mul(a, a, mod); b >>= 1; } return res; } template T mod_inv(T a, T mod){ T u[] = {a, 1, 0}, v[] = {mod, 0, 1}, t; while(*v){ t = *u / *v; swap(u[0] -= t * v[0], v[0]); swap(u[1] -= t * v[1], v[1]); swap(u[2] -= t * v[2], v[2]); } u[1] %= mod; return (u[1] < 0) ? (u[1] + mod) : u[1]; } bool flag; template T garner(const vector& a, vector p, const T mod){ const unsigned int sz = a.size(); vector kp(sz + 1, 0), rmult(sz + 1, 1); p.push_back(mod); for(unsigned int i = 0; i < sz; ++i){ T x = mod_mul(a[i] - kp[i], mod_inv(rmult[i], p[i]), p[i]); x = (x < 0) ? (x + p[i]) : x; for(unsigned int j = i + 1; j < sz + 1; ++j){ kp[j] = mod_add(kp[j], rmult[j] * x, p[j]); rmult[j] = mod_mul(rmult[j], p[i], p[j]); } } if(flag) return rmult[sz]; return kp[sz]; } vector prime; bool is_prime[MAX_N]; void sieve(int n){ for(int i=0;i<=n;i++){ is_prime[i] = true; } is_prime[0] = is_prime[1] = false; for(int i=2;i<=n;i++){ if(is_prime[i]){ prime.push_back(i); for(int j=2*i;j<=n;j+=i){ is_prime[j] = false; } } } } signed main() { cin.tie(0); ios::sync_with_stdio(false); int n; cin >> n; sieve(32000); UnorderedMap mp; flag = true; rep(i,n){ int x, y; cin >> x >> y; if(x) flag = false; for(int p : prime){ if(y % p) continue; int mult = 1; do{ y /= p, mult *= p; }while(y % p == 0); mp[p].emplace_back(x % mult, mult); } if(y > 1) mp[y].emplace_back(x % y, y); } vl x, y; for(const auto& it : mp){ int a = 0, b = 0; for(const P& p : it.se){ if(a < p.se) a = p.se, b = p.fi; } for(const P& p : it.se){ if(p.fi != b % p.se){ cout << "-1\n"; return 0; } } x.pb(b), y.pb(a); } cout << garner(x, y, (long long)MOD) << "\n"; return 0; }