def reconstruct_polynomial(alpha, poly_alpha, field_value=257):
temp_poly = Polynomial([0])
t = len(alpha)
for i in range(t):
poly = Polynomial([1])
temp_prod = 1
alpha_i = alpha[i]
for j in range(t):
if (i != j):
poly = poly.multiply(
Polynomial([1, (field_value - alpha[j]) % field_value]))
temp_prod = temp_prod * (
(alpha_i - alpha[j] + field_value) % field_value)
temp_prod %= field_value
poly = poly.divide_by_constant(temp_prod)
poly = poly.multiply(Polynomial([poly_alpha[i]]))
temp_poly = temp_poly.add(poly)
return temp_poly
