\(ax_1+by_1=gcd(a,b)\)
\(bx_2+(a \mod b)y_2=gcd(b,a \mod b)\)
\(\because gcd(a,b)=gcd(b,a\mod b)\)
\(\therefore ax_1+by_1=bx_2+(a\mod b)y_2\)
\(\because a\mod b=a-\lfloor \frac{a}{b}\rfloor b\)
\(\therefore ax_1+by_1=bx_2+ay_2-\lfloor \frac{a}{b}\rfloor by_2=ay_2+b(x_2-\lfloor\frac{a}{b}\rfloor y_2)\)
\(\therefore x_1=y_2,y_1=x_2-\lfloor\frac{a}{b}\rfloor y_2,x1，y1为当前层，x2,y2为递归的下一层的值\)
\(\because 最后一层,a=g,b=0,ax+by=g\)
\(\therefore 设x=1,y=0\)
int exgcd(int a, int b, int &x, int &y) {
if (!b) {
x = 1;
y = 0;
return a;
}
int d = Exgcd(b, a % b, x, y);
int t = x;
x = y;
y = t - (a / b) * y;
return d;
}