// a * x + b * y = gcd(a, b)
long long extGcd(long long a, long long b, long long& x, long long& y) {
if (b == 0) {
x = 1;
y = 0;
return a;
} else {
int g = extGcd(b, a % b, y, x);
y -= a / b * x;
return g;
}
}
LL congruence( LL r1, LL m1, LL r2, LL m2)
{
extGcd(m1,m2);
if( (r1 - r2 ) % G != 0) return -1;
LL M = m1 * m2 / G; // Solution exists and is unique on LCM(m1,m2) = M
LL K = ( r2 - r1) / G;
LL ans = ((K * m1 * coeffA ) + r1) % M; // Note that K * (m1*coeffA + m2*coeffB) = r2-r1
if( ans < 0) ans += M;
return ans;
}
void extGcd(LL a, LL b)
{
if( b == 0 )
{
G = a;
coeffA = 1; coeffB = 0;
}
else
{
extGcd(b, a % b);
coeffA -= coeffB * (a/b);
swap(coeffA, coeffB);
}
}
int extGcd(int a, int b, int& x, int& y) { // returns d=gcd(a,b) and give x,y such that ax+by=d
if (a == 0) {
x = 0;
y = 1;
return b;
}
int a1, b1, c, x1, y1, rst;
a1 = b % a;
b1 = a;
c = b / a;
rst = extGcd(a1, b1, x1, y1);
x = y1 - c * x1;
y = x1;
return rst;
}
// ASSUME: gcd(a, m) == 1
long long modInv(long long a, long long m) {
long long x, y;
extGcd(a, m, x, y);
return (x % m + m) % m;
}
