gcd.cpp

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define pb push_back
#define mp make_pair
#define all(a) begin(a),end(a)
#define FOR(x,val,to) for(int x=(val);x<int((to));++x)
#define FORE(x,val,to) for(auto x=(val);x<=(to);++x)
#define FORR(x,arr) for(auto &x: arr)
#define FORS(x,plus,arr) for(auto x = begin(arr)+(plus); x != end(arr); ++x)
#define FORREV(x,plus,arr) for(auto x = (arr).rbegin()+(plus); x !=(arr).rend(); ++x)
#define REE(s_) {cout<<s_<<'\n';exit(0);}
#define GET(arr) for(auto &i: (arr)) sc(i)
#define whatis(x) cerr << #x << " is " << x << endl;
#define e1 first
#define e2 second
#define INF 0x7f7f7f7f
typedef std::pair<int,int> pi;
typedef std::vector<int> vi;
typedef std::vector<std::string> vs;
typedef int64_t ll;
typedef uint64_t ull;
#define umap unordered_map
#define uset unordered_set
using namespace std;
using namespace __gnu_pbds;

#ifdef _WIN32
#define getchar_unlocked() _getchar_nolock()
#define _CRT_DISABLE_PERFCRIT_LOCKS
#endif
template<class T> ostream& operator<<(ostream &os, vector<T> V) { os<<"[";for(auto const &vv:V)os<<vv<<","; os<<"]"; return os; }
template<class L, class R> ostream& operator<<(ostream &os, pair<L, R> P) { os<<"("<<P.first<<","<<P.second<<")"; return os; }
inline int fstoi(const string &str){auto it=str.begin();bool neg=0;int num=0;if(*it=='-')neg=1;else num=*it-'0';++it;while(it<str.end()) num=num*10+(*it++-'0');if(neg)num*=-1;return num;}
inline void getch(char &x){while(x = getchar_unlocked(), x < 33){;}}
inline void getstr(string &str){str.clear(); char cur;while(cur=getchar_unlocked(),cur<33){;}while(cur>32){str+=cur;cur=getchar_unlocked();}}
template<typename T> inline bool sc(T &num){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){if(c == EOF) return false;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; return true;}template<typename T, typename ...Args> inline void sc(T &num, Args &...args){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; sc(args...); }
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; //s.find_by_order(), s.order_of_key() <- works like lower_bound
template<typename T> using ordered_map = tree<T, int, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

int x,y,d;
inline void gcd(int a, int b){  //extended euclid, d is gcd, x and y are parameters
    if(!b){                     //(first solution to ax + by = c i.e 25x + 18y = 839)
        d = a;
        x = 1;
        y = 0;
        return;
    }
    gcd(b, a%b);
    int x1 = y;
    int y1 = x - (a/b) * y;
    x = x1;
    y = y1;
}

int main(){
    ios_base::sync_with_stdio(0);cin.tie(0);
    //ax + by = c
    int a,b,c;
    a = 25;
    b = 18;
    c = 839;
    /* cin >> a >> b >> c; */
    gcd(a,b);
    if(c%d)
        cout << "No solutions", exit(0);
    x *= c/d;
    y *= c/d;
    int x1 = x, y1 = y;
    //x1 = x+i*(b/d)
    //y1 = y-i*(a/d)
    /* while((x1|y1) & (1 << 31)){ //while both are non-negative //could make these into equations and solve it for better speed but whatever //or 2 binary searches */
    /*     x1 += b/d; */
    /*     y1 -= a/d; */
    /* } */ //actually let's do it nicer
    //x + i*(b/d) >= 0
    //i >= -x*(d/b) //what if d/b is negative>
    int i = -x/(b/d)+1;
    whatis(i)
    x1 = x+i*(b/d);
    y1 = y-i*(a/d); //first result, for last could use binary search, or equation
    cout << x1 << ' ' << y1 << '\n';
}