//#include #include #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") using namespace std; /*----------------------------------ここからマクロ----------------------------------*/ #define all(a) (a).begin(),(a).end() #define rall(a) (a).rbegin(),(a).rend() #define vecin(a) rep(i,a.size())cin >> a[i] #define overload4(_1,_2,_3,_4,name,...) name /*#define rep1(n) for(int i=0;i<(int)n;++i) #define rep2(i,n) for(int i=0;i<(int)n;++i) #define rep3(i,a,b) for(int i=(int)a;i<(int)b;++i) #define rep4(i,a,b,c) for(int i=(int)a;i<(int)b;i+=(int)c)*/ #define rep1(n) for(ll i=0;i<(ll)n;++i) #define rep2(i,n) for(ll i=0;i<(ll)n;++i) #define rep3(i,a,b) for(ll i=(ll)a;i<(ll)b;++i) #define rep4(i,a,b,c) for(int i=(ll)a;i<(ll)b;i+=(ll)c) #define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__) #ifdef _DEBUG #define debug1(a) cerr << #a << ": " << a << "\n" #define debug2(a,b) cerr << #a << ": " << a << ", " << #b << ": " << b << "\n" #define debug3(a,b,c) cerr << #a << ": " << a << ", " << #b << ": " << b << ", " << #c << ": " << c << "\n" #define debug4(a,b,c,d) cerr << #a << ": " << a << ", " << #b << ": " << b << ", " << #c << ": " << c << ", " << #d << ": " << d << "\n" #define debug(...) overload4(__VA_ARGS__,debug4,debug3,debug2,debug1)(__VA_ARGS__) #define vecout(a) cerr << #a << ": [";rep(i,a.size()){cerr << a[i];cerr << (i == a.size() - 1 ? "":",");}cerr << "]\n" #else #define debug(...) #define vecout(a) #endif #define mp make_pair //struct doset{doset(int n){cout << fixed << setprecision(n);cerr << fixed << setprecision(n);}}; //struct myset{myset(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);}}; void myset(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);} void doset(int n){cout << fixed << setprecision(n);} using ll = long long; using ld = long double; using dou = double; const int inf = 1 << 30; const ll INF = 1LL << 60; const ld pi = 3.14159265358; const ll mod1 = 1000000007LL; const ll mod2 = 998244353LL; typedef pair P; template inline bool chmin(T& a, const U& b){ if(a > b){ a = b; return 1; } return 0; } template inline bool chmax(T& a, const U& b){ if(a < b){ a = b; return 1; } return 0; } //nのm乗をMODで割ったあまりO(logm) ll modpow(ll n,ll m,ll MOD){ if(m == 0)return 1; if(m < 0)return 0; ll res = 1; n %= MOD; while(m){ if(m & 1)res = (res * n) % MOD; m >>= 1; n *= n; n %= MOD; } return res; } ll mypow(ll n,ll m){ if(m == 0)return 1; if(m < 0)return -1; ll res = 1; while(m){ if(m & 1)res = (res * n); m >>= 1; n *= n; } return res; } //素数判定O(sqrt(N)) template inline bool isp(T n){ bool res = true; if(n == 1 || n == 0)return false; else{ for(ll i = 2;i * i <= n;i++){ if(n % i == 0){ res = false; break; } } return res; } } inline bool Yes(bool b = 1){cout << (b ? "Yes\n":"No\n");return b;} inline bool YES(bool b = 1){cout << (b ? "YES\n":"NO\n");return b;} map primefactor(ll n){ map ma; if(n <= 1)return ma; ll m = n; for(ll i = 2;i * i <= n;i++){ while(m % i == 0){ ma[i]++; m /= i; } } if(m != 1)ma[m]++; return ma; } ll __lcm(ll a,ll b){ return a / __gcd(a,b) * b; } template struct fac_solver{ private: ll cmax; vector fac,finv,inv; public: fac_solver(ll n = 100000):cmax(n),fac(n),finv(n),inv(n){ fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (ll i = 2; i < cmax; i++){ fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } //二項係数計算nCk ll nCk(ll n, ll k){ if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD; } ll nPk(ll n,ll k){ if(n < k || n < 0 || k < 0)return 0; return fac[n] * finv[n - k] % MOD; } ll stair_pow(ll n){return fac[n];} }; /*----------------------------------マクロここまで----------------------------------*/ struct rat{ ll ue,si; int sign; rat(ll ue_ = 0,ll si_ = 1){ ll G = __gcd(ue_,si_); ue_ /= G;si_ /= G; sign = 1; if(ue_ < 0 || si_ < 0)sign = -1; ue = abs(ue_);si = abs(si_); } rat operator-()const{ rat res(*this); res.sign *= -1; return res; } rat ABS()const{ rat res(*this); res.sign = 1; return res; } void operator=(const rat& x){ ue = x.ue;si = x.si;sign = x.sign; } rat &operator+=(const rat& x){ if(sign != x.sign){ *this -= (-x); return *this; } ll G = __gcd(si,x.si); ue = ue * (x.si / G) + x.ue * (si / G); ll G1 = __gcd(si,ue); si /= G1;ue /= G1; ll G2 = __gcd(x.si,ue); ue /= G2; si = x.si / G2 * si * G; return *this; } rat &operator-=(const rat& x){ if(sign != x.sign){ *this += (-x); return *this; } ll G = __gcd(si,x.si); ue = ue * (x.si / G) - x.ue * (si / G); if(ue < 0){ sign *= -1; ue = -ue; } ll G1 = __gcd(si,ue); si /= G1;ue /= G1; ll G2 = __gcd(x.si,ue); ue /= G2; si = x.si / G2 * si * G; return *this; } rat operator+(const rat& x)const{ return rat(*this) += x; } rat operator-(const rat& x)const{ return rat(*this) -= x; } rat &operator*=(const rat& x){ sign *= x.sign; ll G1 = __gcd(ue,x.si),G2 = __gcd(si,x.ue); rat X = x; ue /= G1;X.si /= G1;si /= G2;X.ue /= G2; ue *= X.ue;si *= X.si; return *this; } rat operator*(const rat& x)const{ return rat(*this) *= x; } rat inv()const{ rat res(*this); swap(res.ue,res.si); return res; } rat operator/(const rat& x)const{ return rat(*this) *= x.inv(); } void operator/=(const rat& x){ *this = *this / x; } bool operator==(const rat& x)const{return ue == x.ue && si == x.si && sign == x.sign;} bool operator!=(const rat& x)const{return !(rat(*this) == x);} bool operator<(const rat& x)const{ if(sign != x.sign)return sign < x.sign; if(sign == -1){ ll G = __gcd(si,x.si); return ue * (x.si / G) > x.ue * (si / G); } else{ ll G = __gcd(si,x.si); return ue * (x.si / G) < x.ue * (si / G); } } bool operator<=(const rat& x)const{ return rat(*this) == x || rat(*this) < x; } bool operator>(const rat& x)const{ return !(rat(*this) <= x); } bool operator>=(const rat& x)const{ return !(rat(*this) < x); } ll modexpr(const ll M){ return ue % M * modpow(si,M - 2,M) % M; } ld approximation(){ return (ld)(ue) / (ld)(si) * sign; } friend istream& operator>>(istream& is,rat& x){ ll u,s; is >> u >> s; rat res(u,s); x = res; return is; } friend ostream& operator<<(ostream& os,const rat& x){ if(x.sign == -1)os << "-"; os << x.ue << " / " << x.si; return os; } }; vectorsimultaneous_equations(vector> &kei,vector &cns){ int sz = kei.size(); if(sz == 1){ return {cns[0] / kei[0][0]}; } vector> nextk(sz - 1,vector(sz - 1)); vector nextc(sz - 1); rep(i,sz - 1){//上を下に合わせる if(kei[i][0] == 0){ rep(j,sz - 1){ nextk[i][j] = kei[i][j + 1]; } nextc[i] = cns[i]; } else{ rat ret = kei[i + 1][0] / kei[i][0]; rep(j,sz - 1){ nextk[i][j] = kei[i][j + 1] * ret - kei[i + 1][j + 1]; } nextc[i] = cns[i] * ret - cns[i + 1]; } } auto na = simultaneous_equations(nextk,nextc); rat finalcns = cns[0]; rep(i,1,sz){ finalcns -= kei[0][i] * na[i - 1]; } na.insert(na.begin(),finalcns / kei[0][0]); return na; } int main(){ myset(); ll a,b,c,d,e,f; cin >> a >> b >> c >> d >> e >> f; vector> test(2,vector(2)); vector cns(2); cns[0] = rat(c);cns[1] = rat(f); test[0][0] = rat(a);test[0][1] = rat(b);test[1][0] = rat(d);test[1][1] = rat(e); auto ans = simultaneous_equations(test,cns); doset(10); cout << ans[0].approximation() << " " << ans[1].approximation() << "\n"; //vector> vec = {{2,1}};vector v2 = {{8,1}}; //cout << simultaneous_equations(vec,v2)[0] << "\n"; }