#include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pld = pair; const int INF=1e9+7; const ll LINF=9223372036854775807; const ll MOD=1e9+7; const ld PI=acos(-1); const ld EPS = 1e-10; //微調整用(EPSより小さいと0と判定など) int ii() { int x; if (scanf("%d", &x)==1) return x; else return 0; } long long il() { long long x; if (scanf("%lld", &x)==1) return x; else return 0; } string is() { string x; cin >> x; return x; } char ic() { char x; cin >> x; return x; } void oi(int x) { printf("%d ", x); } void ol(long long x) { printf("%lld ", x); } void od_nosp(double x) { printf("%.15f", x); } // 古い問題用 void od(double x) { printf("%.15f ", x); } void os(const string &s) { printf("%s ", s.c_str()); } void oc(const char &c) { printf("%c ", c); } #define o_map(v){cerr << #v << endl; for(const auto& xxx: v){cout << xxx.first << " " << xxx.second << "\n";}} //動作未確認 void br() { putchar('\n'); } // #define gcd __gcd //llは受け取らない C++17~のgcdと違うので注意 // int lcm(int a, int b){return a / gcd(a, b) * b;} #define b_e(a) a.begin(),a.end() //sort(b_e(vec)); #define REP(i,m,n) for(ll i=(ll)(m) ; i < (ll)(n) ; i++ ) #define DREP(i,m,n) for(ll i=(ll)(m) ; i > (ll)(n) ; i-- ) #define rep(i,n) REP(i,0,n) #define m_p(a,b) make_pair(a,b) #define p_b push_back #define SZ(x) ((ll)(x).size()) //size()がunsignedなのでエラー避けに #define endk '\n' // coutによるpairの出力(空白区切り) template ostream& operator<<(ostream& s, const pair& p) {return s << "(" << p.first << " " << p.second << ")";} // coutによるvectorの出力(空白区切り) template ostream& operator<<(ostream& s, const vector& v) { int len = v.size(); for (int i = 0; i < len; ++i) { s << v[i]; if (i < len - 1) s << " "; //"\t"に変えるとTabで見やすく区切る } return s; } // coutによる多次元vectorの出力(空白区切り) template ostream& operator<<(ostream& s, const vector< vector >& vv) { int len = vv.size(); for (int i = 0; i < len; ++i) { s << vv[i] << endl; } return s; } //最大値、最小値の更新。更新したor等しければtrueを返す template bool chmax(T& a, T b){return (a = max(a, b)) == b;} template bool chmin(T& a, T b){return (a = min(a, b)) == b;} //4近傍(上下左右) rep(i, 2) にすると右・下だけに進む vector dx_4 = {1, 0, -1, 0}; vector dy_4 = {0, 1, 0, -1}; // -------- template end - // // - library ------------- // // #include #include #include #include #include #include namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast moduler by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m` barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; for (long long a : {2, 7, 61}) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(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 (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); } // namespace internal } // namespace atcoder namespace atcoder { long long pow_mod(long long x, long long n, int m) { assert(0 <= n && 1 <= m); if (m == 1) return 0; internal::barrett bt((unsigned int)(m)); unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m)); while (n) { if (n & 1) r = bt.mul(r, y); y = bt.mul(y, y); n >>= 1; } return r; } long long inv_mod(long long x, long long m) { assert(1 <= m); auto z = internal::inv_gcd(x, m); assert(z.first == 1); return z.second; } // (rem, mod) std::pair crt(const std::vector& r, const std::vector& m) { assert(r.size() == m.size()); int n = int(r.size()); // Contracts: 0 <= r0 < m0 long long r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1) // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1)); // r2 % m0 = r0 // r2 % m1 = r1 // -> (r0 + x*m0) % m1 = r1 // -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1) // -> x = (r1 - r0) / g * inv(u0) (mod u1) // im = inv(u0) (mod u1) (0 <= im < u1) long long g, im; std::tie(g, im) = internal::inv_gcd(m0, m1); long long u1 = (m1 / g); // |r1 - r0| < (m0 + m1) <= lcm(m0, m1) if ((r1 - r0) % g) return {0, 0}; // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1) long long x = (r1 - r0) / g % u1 * im % u1; // |r0| + |m0 * x| // < m0 + m0 * (u1 - 1) // = m0 + m0 * m1 / g - m0 // = lcm(m0, m1) r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if (r0 < 0) r0 += m0; } return {r0, m0}; } long long floor_sum(long long n, long long m, long long a, long long b) { long long ans = 0; if (a >= m) { ans += (n - 1) * n * (a / m) / 2; a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } long long y_max = (a * n + b) / m, x_max = (y_max * m - b); if (y_max == 0) return ans; ans += (n - (x_max + a - 1) / a) * y_max; ans += floor_sum(y_max, a, m, (a - x_max % a) % a); return ans; } } // namespace atcoder using namespace atcoder; // --------- library end - // int main(){ vector rs(3); vector ms(3); rep(i, 3){ rs[i] = il(); ms[i] = il(); } pll p = crt(rs, ms); if (p.second == 0) cout << -1 << endk; else cout << p.first; }