Given two Constrained Equation x1<= a1*x+b1*y <=x2 y1<= a2*x+b2*y <=y2

Find number of solution of (x11,y11) for x1<= x11 <= x2 and y1<= y11 <=y2 and simultaneous equation a1*x+b1*y = x11 and a2*x+b2*y=y11 both give integral solution of x and y . x1,x2,y1,y2 ranges are 1e9