import math

def circle_circle_intersection(x0, y0, r0, x1, y1, r1):
    d = math.hypot(x1 - x0, y1 - y0)
    if d > r0 + r1:
        return []  # No intersection.
    if d < abs(r0 - r1):
        return []  # One circle is contained within the other.
    if d == 0 and r0 == r1:
        return []  # Circles are coincident.
    else:
        a = (r0**2 - r1**2 + d**2) / (2 * d)
        h = math.sqrt(max(0, r0**2 - a**2))
        x2 = x0 + a * (x1 - x0) / d
        y2 = y0 + a * (y1 - y0) / d
        rx = -(y1 - y0) * (h / d)
        ry = -(x1 - x0) * (h / d)
        xi1 = x2 + rx
        xi2 = x2 - rx
        yi1 = y2 - ry
        yi2 = y2 + ry
        return [(xi1, yi1), (xi2, yi2)]

def compute_total_distance(n, r, points):
    O_x, O_y = 0.0, 0.0  # Assuming the circle is centered at (0, 0).
    total_length = 0.0
    for i in range(n):
        P_i = points[i]
        P_next = points[(i + 1) % n]
        s_x, s_y = P_next[0] - P_i[0], P_next[1] - P_i[1]
        s_angle = math.atan2(s_y, s_x)
        # Circle centered at P_i
        r0 = math.hypot(s_x, s_y)
        x0, y0 = P_i[0], P_i[1]
        # Circle centered at O
        r1 = r
        x1, y1 = O_x, O_y
        intersections = circle_circle_intersection(x0, y0, r0, x1, y1, r1)
        min_theta = None
        for xi, yi in intersections:
            v_x, v_y = xi - P_i[0], yi - P_i[1]
            v_angle = math.atan2(v_y, v_x)
            theta = (s_angle - v_angle) % (2 * math.pi)
            if theta <= 0:
                theta += 2 * math.pi
            if min_theta is None or theta < min_theta:
                min_theta = theta
        if min_theta is not None:
            d_i1 = math.hypot(points[0][0] - P_i[0], points[0][1] - P_i[1])
            total_length += d_i1 * min_theta
        else:
            continue  # No valid rotation, skip.
    return total_length

# Read input
n, r = map(float, input().split())
n = int(n)
points = [tuple(map(float, input().split())) for _ in range(n)]

# Compute and print the total distance
total_distance = compute_total_distance(n, r, points)
print(total_distance)