def c(a, xx, dy):
	 x = len(a) - 1
	 ans = dy[0]
	 prevx = xx - a[len(a) - 1]
	 f = 1
	 y = 2
	 line = str(ans)
	 pLine = "(" + str(xx) + " - " + str(a[len(a) - 1]) + ")"
	 while True:
		 ans = ans + ((dy[y-1]/ ((abs(a[0] - a[1])**(y - 1)) * f)) * (prevx))
		 line = line + " + " + "(" + "(" + str(dy[y-1]) + "/" + "((|" + str(a[0]) + " - " +  str(a[1]) + "|" + "**(" + str(y - 1) + ")) * " + str(f) + ")" + ")" + " * " + pLine
		 x = x - 1
		 print(line)
		 if x == 0:
			 break
		 f = f * y
		 y = y + 1
		 prevx = prevx * (xx - a[x])
		 pLine = pLine + " * " + "(" + str(xx) + " - " + str(a[x]) + ")"
	 return ans

def da(a):
	b = []
	for x in range(0, len(a)):
		b.append([])
		for y in range(0, len(a)):
			b[x].append([0])
		b[0][x] = a[x]
	for x in range(1, len(a)):
		for y in range(0, len(a) - x):
			b[x][y] = b[x - 1][ y + 1] - b[x - 1][ y]
	g = []
	for x in range(0, len(a)):
		g.append(b[x][len(a) - x - 1])
	return g

c([-1, 0, 1, 2], 0.5, da([-0.5, 0, 2, 8]))