#line 1 "c.cpp" #include #include #define rep(i,n) for (int i = 0; i < int(n); ++i) #define repp(i,n,m) for (int i = m; i < int(n); ++i) #define repb(i,n) for (int i = int(n)-1; i >= 0; --i) #define all(v) v.begin(),v.end() using namespace std; using namespace atcoder; using ll = long long; using ull = unsigned long long; using ld = long double; using P = pair; using PL = pair; using pdd = pair; using pil = pair; using pli = pair; templateistream &operator>>(istream &is,vector &v){for(auto &e:v)is>>e;return is;} templatebool range(T a,T b,T x){return (a<=x&&xbool rrange(T a,T b,T c,T d,T x,T y){return (range(a,c,x)&&range(b,d,y));} templatevoid rev(vector &v){reverse(v.begin(),v.end());} void revs(string &s) {reverse(s.begin(),s.end());} templatevoid sor(vector &v, int f=0){sort(v.begin(),v.end());if(f!=0) rev(v);} templatebool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;} templatebool chmax(T &a,const T &b){if(avoid uniq(vector &v){sor(v);v.erase(unique(v.begin(),v.end()),v.end());} templatevoid print(pair a); templatevoid print(vector v); templatevoid print(vector> v); void print(){ putchar(' '); } void print(bool a){ printf("%d", a); } void print(int a){ printf("%d", a); } void print(long a){ printf("%ld", a); } void print(long long a){ printf("%lld", a); } void print(char a){ printf("%c", a); } void print(char a[]){ printf("%s", a); } void print(const char a[]){ printf("%s", a); } void print(long double a){ printf("%.15Lf", a); } void print(const string& a){ for(auto&& i : a) print(i); } void print(unsigned int a){ printf("%u", a); } void print(unsigned long long a) { printf("%llu", a); } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } templatevoid print(pair a){print(a.first);print(),print(a.second);} templatevoid print(vector v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())print();}} templatevoid print(vector> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())out();}} void yes(){out("Yes");} void no (){out("No");} void yn (bool t){if(t)yes();else no();} void fast_io(){cin.tie(0); ios::sync_with_stdio(0); cout< dx = {0,1,0,-1,1,1,-1,-1}; const vector dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; } // namespace noya2 using namespace noya2; using mint = modint998244353; void out(mint a){out(a.val());} void out(vector a){vector b(a.size()); rep(i,a.size()) b[i] = a[i].val(); out(b);} void out(vector> a){for (auto v : a) out(v);} istream &operator>>(istream &is,vector &v){for(auto &e:v){ll _x;is>>_x;e=_x;}return is;} #line 2 "math.hpp" #line 6 "math.hpp" namespace noya2{ using namespace std; using ll = long long; ll safe_mod(ll a, ll m){ // m >= 1, 0 <= safe_mod(a,m) < m, safe_mod(a,m) = a (mod m) ll res = a % m; if (res < 0) res += m; return res; } struct math{ static ll gcd(ll a, ll b){return b?gcd(b,a%b):a;} static void ext_gcd1_plus(ll a, ll b, ll &x, ll &y){ // gcd(a,b) = 1, a >= 0, b >= 0, ax + by = 1 if (b == 0){ // a = 1 x = 1, y = 0; return ; } ext_gcd1_plus(b, a%b, y, x); x = safe_mod(x,b); y = (1 - a * x) / b; } static void ext_gcd1_minus(ll a, ll b, ll &x, ll &y){ // gcd(a,b) = 1, a >= 0, b >= 0, ax - by = 1 if (b == 0){ // a = 1 x = 1, y = 0; return ; } ext_gcd1_plus(b, a%b, y, x); x = safe_mod(x,b); y = (a * x - 1) / b; } }; ll safe_gcd(ll a, ll b){return math::gcd(abs(a),abs(b));} // safe_gcd(0,0) = 0, safe_gcd(c,0) = safe_gcd(0,c) = c ll safe_lcm(ll a, ll b){return abs(a) / safe_gcd(a,b) * abs(b);} struct line{ ll a, b, c; // ax + by = c void norm(){ // a >= 0, if (a == 0) -> b >= 0, gcd(a,b,c) = 1 if (a < 0) a = -a, b = -b, c = -c; if (a == 0) if (b < 0) b = -b, c = -c; ll g = safe_gcd(safe_gcd(a,b),c); a /= g, b /= g, c /= g; } line (ll _a = 1, ll _b = 0, ll _c = 0) : a(_a), b(_b), c(_c) { assert(_a != 0 || _b != 0); norm(); } line (ll x1, ll y1, ll x2, ll y2){ // --- (x1,y1) --- (x2,y2) --- assert(x1 != x2 || y1 != y2); ll wx = x2 - x1, wy = y2 - y1; ll wg = safe_gcd(wx,wy); a = wy / wg, b = -wx / wg; c = a * x1 + b * y1; norm(); } static line get_line(ll x1, ll y1, ll ex, ll ey){ // y = ey/ex (x - x1) + y1 return line(ey,-ex,ey*x1-ex*y1); } static line vertical_line(ll x1, ll y1, ll x2, ll y2){ // perpendicular bisector ll ex = y2 - y1, ey = x1 - x2; return line(ey*2,-ex*2,ey*(x1+x2)-ex*(y1+y2)); } bool operator<(const line &rhs) const { return vector{a,b,c} < vector{rhs.a,rhs.b,rhs.c}; // to use set or map for line } }; pair ext_gcd(ll a, ll b, ll c){ // ax + by = c, |a|,|b|,|c| < 1e9, x <= max(|B|,|C|), y<= max(|A|,|C|) if (a < 0) return ext_gcd(-a,-b,-c); if (c < 0){ pair res = ext_gcd(a,b,-c); res.first = -res.first, res.second = -res.second; return res; } if (c == 0) return pair(0,0); if (a == 0 && b == 0) return pair(0,0); // answer not exist ll g = safe_gcd(a,b); if (c % g != 0) return pair(0,0); // answer not exist a /= g, b /= g, c /= g; ll x, y; if (b == 0) return pair(c,0); if (b > 0) math::ext_gcd1_plus(a,b,x,y); else math::ext_gcd1_minus(a,-b,x,y); x = safe_mod(x*c,abs(b)); y = (c - a * x) / b; return pair(x,y); } template T safe_ceil(T p, T q); template T safe_floor(T p, T q){ if (q < T(0)) return safe_floor(-p,-q); if (p >= T(0)) return p / q; return -safe_ceil(-p,q); } template T safe_ceil(T p, T q){ if (q < T(0)) return safe_ceil(-p,-q); if (p >= T(0)) return (p + q - 1) / q; return -safe_floor(-p,q); } struct Eratosthenes{ static vector table; Eratosthenes (int Nmax = -1) {init(Nmax);} static void init(int Nmax){ if (!table.empty()) return ; table.resize(Nmax+1,0); table[0] = 1, table[1] = 1; for (int p = 2; p <= Nmax; p++){ if (table[p] != 0) continue; for (int j = p; j <= Nmax; j += p){ table[j] = p; } } } }; vectorEratosthenes::table = vector(0); void build_eratosthenes(const int Nmax){Eratosthenes::init(Nmax);} vector> fast_prime_factorization(int N){ int pre = -1, cnt = 0; vector> res; while(true) { if (N == 1){ if (cnt > 0) res.emplace_back(pre,cnt); break; } int div = Eratosthenes::table[N]; if (pre != div){ if (cnt > 0) res.emplace_back(pre,cnt); pre = div, cnt = 1; } else cnt++; N /= div; } return res; } bool fast_is_prime(int N){ if (N <= 1) return false; return Eratosthenes::table[N] == N; } vector> prime_factorization(ll N){ vector> res; ll iN = N; for (ll d = 2; d * d <= N; d++){ if (iN % d != 0) continue; if (iN == 1) break; int ie = 0; while (iN % d == 0) iN /= d, ie++; res.emplace_back(d,ie); } if (iN != 1) res.emplace_back(iN,1); return res; } }// namespace noya2 #line 78 "c.cpp" void calc(vector &res, ll &a, ll &b){ if (b == 0) return ; if (a == 0){ res.emplace_back(pil(1,1)); a = b; res.emplace_back(pil(2,-1)); b = 0; return ; } if (a == b){ res.emplace_back(pil(2,-1)); b = 0; return ; } if (a > b){ res.emplace_back(pil(1,-a/b)); a -= a/b*b; calc(res,a,b); } else { res.emplace_back(pil(2,-b/a)); b -= b/a*a; calc(res,a,b); } } void solve(){ ll a1, b1, a2, b2; cin >> a1 >> b1 >> a2 >> b2; ll c1 = a1, d1 = b1, c2 = a2, d2 = b2; ll g1 = safe_gcd(a1,b1), g2 = safe_gcd(a2,b2); if (g1 != g2){ out(-1); return ; } vector v1, v2; const ll mx = 500000000; auto change = [&](bool pre){ ll &a = (pre ? a1 : a2); ll &b = (pre ? b1 : b2); auto &v = (pre ? v1 : v2); if (a < 0){ if (b > 0){ ll p = mx/b; v.emplace_back(pil(1,p)); a += b * p; } else if (b < 0){ ll p = mx/(-b); v.emplace_back(pil(1,-p)); a -= b * p; } else { v.emplace_back(pil(2,-1)); b = -a; v.emplace_back(pil(1,1)); a = 0; } } if (b < 0){ if (a > 0){ ll p = mx/a; v.emplace_back(pil(2,p)); b += a * p; } else { v.emplace_back(pil(1,-1)); a = -b; v.emplace_back(pil(2,1)); b = 0; } } }; change(true); change(false); calc(v1,a1,b1); calc(v2,a2,b2); int siz = v2.size(); repb(i,siz) v1.emplace_back(pil(v2[i].first,-v2[i].second)); out((int)v1.size()); for (auto p : v1) out(p); for (auto p : v1){ if (p.first == 1) c1 += d1 * p.second; else d1 += c1 * p.second; } assert(c1==c2&&d1==d2); } int main(){ fast_io(); int t = 1; //cin >> t; while(t--) solve(); }