// #pragma GCC optimize("O3,unroll-loops") #include // #include using namespace std; #if __cplusplus >= 202002L using namespace numbers; #endif template struct modular_fixed_base{ #define IS_INTEGRAL(T) (is_integral_v || is_same_v || is_same_v) #define IS_UNSIGNED(T) (is_unsigned_v || is_same_v) static_assert(IS_UNSIGNED(data_t)); static_assert(_mod >= 1); static constexpr bool VARIATE_MOD_FLAG = false; static constexpr data_t mod(){ return _mod; } template static vector precalc_power(T base, int SZ){ vector res(SZ + 1, 1); for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base; return res; } static vector _INV; static void precalc_inverse(int SZ){ if(_INV.empty()) _INV.assign(2, 1); for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]); } // _mod must be a prime static modular_fixed_base _primitive_root; static modular_fixed_base primitive_root(){ if(_primitive_root) return _primitive_root; if(_mod == 2) return _primitive_root = 1; if(_mod == 998244353) return _primitive_root = 3; data_t divs[20] = {}; divs[0] = 2; int cnt = 1; data_t x = (_mod - 1) / 2; while(x % 2 == 0) x /= 2; for(auto i = 3; 1LL * i * i <= x; i += 2){ if(x % i == 0){ divs[cnt ++] = i; while(x % i == 0) x /= i; } } if(x > 1) divs[cnt ++] = x; for(auto g = 2; ; ++ g){ bool ok = true; for(auto i = 0; i < cnt; ++ i){ if(modular_fixed_base(g).power((_mod - 1) / divs[i]) == 1){ ok = false; break; } } if(ok) return _primitive_root = g; } } constexpr modular_fixed_base(){ } modular_fixed_base(const double &x){ data = _normalize(llround(x)); } modular_fixed_base(const long double &x){ data = _normalize(llround(x)); } template::type* = nullptr> modular_fixed_base(const T &x){ data = _normalize(x); } template::type* = nullptr> static data_t _normalize(const T &x){ int sign = x >= 0 ? 1 : -1; data_t v = _mod <= sign * x ? sign * x % _mod : sign * x; if(sign == -1 && v) v = _mod - v; return v; } template::type* = nullptr> operator T() const{ return data; } modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; } modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; } template::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); } template::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); } modular_fixed_base &operator++(){ return *this += 1; } modular_fixed_base &operator--(){ return *this += _mod - 1; } modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; } modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; } modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); } modular_fixed_base &operator*=(const modular_fixed_base &rhs){ if constexpr(is_same_v) data = (unsigned long long)data * rhs.data % _mod; else if constexpr(is_same_v){ long long res = data * rhs.data - _mod * (unsigned long long)(1.L / _mod * data * rhs.data); data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod); } else data = _normalize(data * rhs.data); return *this; } template::type* = nullptr> modular_fixed_base &inplace_power(T e){ if(e == 0) return *this = 1; if(data == 0) return *this = {}; if(data == 1 || e == 1) return *this; if(data == mod() - 1) return e % 2 ? *this : *this = -*this; if(e < 0) *this = 1 / *this, e = -e; if(e == 1) return *this; modular_fixed_base res = 1; for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this; return *this = res; } template::type* = nullptr> modular_fixed_base power(T e) const{ return modular_fixed_base(*this).inplace_power(e); } modular_fixed_base &operator/=(const modular_fixed_base &otr){ make_signed_t a = otr.data, m = _mod, u = 0, v = 1; if(a < _INV.size()) return *this *= _INV[a]; while(a){ make_signed_t t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return *this *= u; } #define ARITHMETIC_OP(op, apply_op)\ modular_fixed_base operator op(const modular_fixed_base &x) const{ return modular_fixed_base(*this) apply_op x; }\ template::type* = nullptr>\ modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\ template::type* = nullptr>\ friend modular_fixed_base operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x) apply_op y; } ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=) #undef ARITHMETIC_OP #define COMPARE_OP(op)\ bool operator op(const modular_fixed_base &x) const{ return data op x.data; }\ template::type* = nullptr>\ bool operator op(const T &x) const{ return data op modular_fixed_base(x).data; }\ template::type* = nullptr>\ friend bool operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x).data op y.data; } COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=) #undef COMPARE_OP friend istream &operator>>(istream &in, modular_fixed_base &number){ long long x; in >> x; number.data = modular_fixed_base::_normalize(x); return in; } //#define _SHOW_FRACTION friend ostream &operator<<(ostream &out, const modular_fixed_base &number){ out << number.data; #if defined(LOCAL) && defined(_SHOW_FRACTION) cerr << "("; for(auto d = 1; ; ++ d){ if((number * d).data <= 1000000){ cerr << (number * d).data; if(d != 1) cerr << "/" << d; break; } else if((-number * d).data <= 1000000){ cerr << "-" << (-number * d).data; if(d != 1) cerr << "/" << d; break; } } cerr << ")"; #endif return out; } data_t data = 0; #undef _SHOW_FRACTION #undef IS_INTEGRAL #undef IS_UNSIGNED }; template vector> modular_fixed_base::_INV; template modular_fixed_base modular_fixed_base::_primitive_root; const unsigned int mod = (119 << 23) + 1; // 998244353 // const unsigned int mod = 1e9 + 7; // 1000000007 // const unsigned int mod = 1e9 + 9; // 1000000009 // const unsigned long long mod = (unsigned long long)1e18 + 9; using modular = modular_fixed_base, mod>; // Requires modular template struct hash_base{ #ifdef LOCAL #define ASSERT(c) assert(c) #else #define ASSERT(c) 42 #endif static modular_t _base, _inv_base; template static void setup(T base = 0){ if constexpr(modular_t::VARIATE_MOD_FLAG) modular_t::setup((unsigned long long)1e18 + 9); if(!base) base = mt19937_64(chrono::high_resolution_clock::now().time_since_epoch().count())() % (long long)1e17 + (long long)9e17; _base = base, _inv_base = modular_t(1) / base; } static vector _power, _inv_power; static void setup_power(size_t len){ if(_power.empty()) _power.push_back(1), _inv_power.push_back(1); while((int)_power.size() <= len){ _power.push_back(_power.back() * _base); _inv_power.push_back(_inv_power.back() * _inv_base); } } static modular_t power(len_t e){ assert(e >= 0); if constexpr(ALLOW_BINEXP) return e < (int)_power.size() ? _power[e] : _base.power(e); else{ if((int)_power.size() <= e) setup_power(e); return _power[e]; } } static modular_t inv_power(len_t e){ assert(e >= 0); if constexpr(ALLOW_BINEXP) return e < (int)_inv_power.size() ? _inv_power[e] : _inv_base.power(e); else{ if((int)_power.size() <= e) setup_power(e); return _inv_power[e]; } } hash_base(){ ASSERT(_base >= 1); } hash_base(const modular_t &x, len_t len): data(x), len(len){ ASSERT(_base >= 1); } template>::type* = nullptr> hash_base(T x): data(x), len(1){ ASSERT(_base >= 1); } template>::type* = nullptr> hash_base(const vector &s){ ASSERT(_base >= 1); for(auto c: s) *this += hash_base(c); } hash_base(const string &s){ ASSERT(_base >= 1); for(auto c: s) *this += hash_base(c); } hash_base &operator=(const hash_base &x){ data = x.data, len = x.len; return *this; } hash_base &operator+=(const hash_base &x){ data = power(x.len) * data + x.data; len += x.len; return *this; } hash_base operator+(const hash_base &x) const{ return hash_base(*this) += x; } hash_base &inplace_append_right(const hash_base &x){ return *this += x; } hash_base append_right(const hash_base &x) const{ return hash_base(*this).inplace_append_right(x); } hash_base &inplace_append_left(const hash_base &x){ data += power(len) * x.data; len += x.len; return *this; } hash_base append_left(const hash_base &x) const{ return hash_base(*this).inplace_append_left(x); } hash_base &inplace_pop_right(const hash_base &x){ assert(len >= x.len); data = inv_power(x.len) * (data - x.data); len -= x.len; return *this; } hash_base pop_right(const hash_base &x) const{ return hash_base(*this).inplace_pop_right(x); } hash_base &inplace_pop_left(const hash_base &x){ assert(len >= x.len); data -= power(len - x.len) * x.data; len -= x.len; return *this; } hash_base pop_left(const hash_base &x) const{ return hash_base(*this).inplace_pop_left(x); } template>::type* = nullptr> hash_base &inplace_update(len_t pos, T x){ assert(0 <= pos && pos < len); data += power(len - pos - 1) * x; return *this; } template>::type* = nullptr> hash_base update(len_t pos, T x) const{ return hash_base(*this).inplace_update(pos, x); } hash_base &inplace_update(len_t pos, const hash_base &x){ assert(0 <= pos && pos + x.len <= len); data += power(len - pos - x.len) * x.data; return *this; } hash_base update(len_t pos, const hash_base &x) const{ return hash_base(*this).inplace_update(pos, x); } #define COMPARE_OP(op)\ bool operator op(const hash_base &x) const{ return data op x.data; } COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=) #undef COMPARE_OP template>::type* = nullptr> hash_base &operator*=(T x){ assert(x >= 0); if(x == 0) return *this = {}; if(x == 1) return *this; hash_base res{}; for(auto e = x; e; e >>= 1){ if(e & 1) res += *this; *this += *this; } return *this = res; } template>::type* = nullptr> hash_base operator*(T x) const{ return hash_base(*this) *= x; } template>::type* = nullptr> friend hash_base operator*(T x, const hash_base &h){ return hash_base(h) *= x; } friend ostream &operator<<(ostream &out, const hash_base &x){ return out << "{" << x.data << ", " << x.len << "}"; } modular_t data = 0; len_t len = 0; #undef ASSERT }; template modular_t hash_base::_base; template modular_t hash_base::_inv_base; template vector hash_base::_power{1}; template vector hash_base::_inv_power{1}; using hash_t = hash_base, int, false>; int main(){ cin.tie(0)->sync_with_stdio(0); cin.exceptions(ios::badbit | ios::failbit); hash_t::setup(); int n, m; cin >> n >> m; vector obj(m); copy_n(istream_iterator(cin), m, obj.begin()); vector card(n, vector(m)); vector opac(n); vector> appear(101); for(auto i = 0; i < n; ++ i){ copy_n(istream_iterator(cin), m, card[i].begin()); cin >> opac[i]; ++ appear[opac[i]][hash_t{card[i]}]; } for(auto i = 0; i < n; ++ i){ hash_t cur{card[i]}; for(auto op = 1; op <= 100; ++ op){ hash_t x; for(auto j = 0; j < m; ++ j){ int value = obj[j] * 100 * 100 - opac[i] * (100 - op) * card[i][j]; if(value % (100 * op)){ goto FAIL; } x += value / 100 / op; } if(appear[op][x] > (x == cur)){ cout << "Yes\n"; return 0; } FAIL:; } } cout << "No\n"; return 0; } /* */