#circlesInCircle.py

import math

#distance between two points, each a tuple of x and y coordinates
def distance_points(pt1,pt2):
    return math.sqrt((pt1[0]-pt2[0])**2 + (pt1[1]-pt2[1])**2)


R = int(input("Enter the radius of the outer circle: "))
r = int(input("Enter the radius of the inner circles: "))

from ezgraphics import GraphicsWindow

margin = 10
size = 2*R
win = GraphicsWindow(size+margin,size+margin)
canvas = win.canvas()
canvas.setColor("red")
canvas.setFill()
canvas.drawOval(margin/2,margin/2,  2*R,2*R)

canvas.setColor("green")
xO = R+margin/2
yO = R+margin/2
canvas.drawOval(xO,yO ,2,2)   #origin

layers = R // (2*r)
for layer in range(layers):
    inner_circumference = 2*math.pi*(R-(2*layer+1)*r)
    canvas.setColor("red")
    canvas.setFill()
    canvas.drawOval((2*layer+1)*r+margin/2,(2*layer+1)*r+margin/2, \
                    2*(R-(2*layer+1)*r),2*(R-(2*layer+1)*r))

    num_circles = inner_circumference // (2*r)
    print("num_circles:",num_circles)
    centers = []
    for p in range(int(num_circles)):
        alpha = 2*math.pi/num_circles * p
        cos_p = math.cos(alpha)
        sin_p = math.sin(alpha)
        x = cos_p*(R-(2*layer+1)*r)
        y = sin_p*(R-(2*layer+1)*r)
        can_fit = True
        
        #innermost layer: if would overlap, rotate to find non-overlapping
        while layer==layers-1 and p>0 and distance_points((x,y),centers[-1])<2*r:
            alpha += math.pi/64   #not perfect...
            cos_p = math.cos(alpha)
            sin_p = math.sin(alpha)
            x = cos_p*(R-(2*layer+1)*r)
            y = sin_p*(R-(2*layer+1)*r)
            if alpha>=2*math.pi or (p>1 and distance_points((x,y),centers[0])<2*r):
                can_fit = False
                break

        if can_fit:    
            centers.append((x,y))
            canvas.setColor("green")
            canvas.setFill()
            canvas.drawOval(centers[-1][0]+(R-r)+margin/2,\
                            (centers[-1][1]+(R-r)+margin/2),  2*r,2*r)
            canvas.setColor("black")
            canvas.drawOval(centers[-1][0]+R+margin/2,(centers[-1][1]+R+margin/2),  2,2)

#can fit a circle at the origin    200 15
if distance_points((0,0), centers[-1]) >= 2*r:
    print("yes")
    canvas.setColor("green")
    canvas.setFill()
    canvas.drawOval(0+(R-r)+margin/2,0+(R-r)+margin/2, 2*r,2*r)