// Returns (x, y) such that ax + by = gcd(a, b)
pll bezout(lint a, lint b) {
if (b == 0) return pll(1, 0);
pll p = bezout(b, a % b);
return pll(p.second, p.first - (a / b) * p.second);
}
void bezout(int a, int b, int *u, int *v){
int q;
if(b==0){
*u=1;
*v=0;
}
else{
q=a/b;
bezout(b,a%b, u, v);
int temp = (*u) - (*v)*q;
*u=*v;
*v=temp;
}
}
/*
coeffs: coefficients
solve: RHS
1. Divide through by GCD(coeffs) (sol to coprime equation = sol to original)
2. Solve babby diophantine to get top left corner = solve/gcd
*/
void dio(int coeffs[], int vars, int solve, int matrix[vars][vars+1] ){
if(1){
printf("Valid!\n");
int geeceedee = lgcd(coeffs,vars);
if( solve % geeceedee == 0 ){
printf("Solutions!\n");
int i;
int coprimes[vars];
for(i=0; i<vars; i++){//coeffs NOW COPRIME. NOW SOLVING FOR solve/geeceedee
coprimes[i]=coeffs[i]/geeceedee;
matrix[i][0]=coprimes[i];
}
for(i=0; i<vars; i++){//1s n 0s
int j;
for(j=1; j<vars+1; j++)
matrix[i][j] = (j==i+1) ? 1 : 0;
}
//SOLVING SHIT (COPRIME MATRIX)//
int g=1;
i=1;
while((solve/geeceedee) % gcd(coprimes[0],coprimes[i]) != 0){//finds coeff[i]: coeff[0]x + coeff[i]y=solve has sol
i++;
}
g=i;
int d=(solve/geeceedee)/gcd(coprimes[0], coprimes[g]/geeceedee);
int u, v;
bezout(coprimes[0], coprimes[g],&u,&v);
u *= d;//coeff[0]u + gv = solve;
v *= d;
for(i=0; i<vars+1; i++)//puts solve in top corner
matrix[0][i] = (u*matrix[0][i]) + (v*matrix[g][i]);
for(i=1; i<vars; i++){//elim row with top row
int j;
int fact = lcm(coprimes[i], matrix[0][0]);
for(j=0; j<vars+1; j++){
matrix[i][j] = (fact/coprimes[i])*matrix[i][j] - (fact/matrix[0][0])*matrix[0][j];
}
}
}
//No Solution
else{
printf("No solution!\n");
}
}
//Bad input
else{
printf("Bad input!\n");
}
}
void init_cle(int P, int Q, cle *publique, cle *prive){
int M = (Q-1)*(P-1);
int N = P*Q;
//printf("\nDonner un C, tel qu'il soit premier avec M (%d) : ", M);
int C = 7;
//scanf("%d", &C);
int u = bezout(C, M);
publique->x = N;
publique->y = C;
prive->x = u;
prive->y = N;
}
