from math import *

# Returns a congruence class of a specified modulus and residue,
# constrained in [lower, upper]
def congruence_class(residue, modulus, lower, upper, order = 'asc'):
    residue = residue % modulus
    strict_lower = (lower//modulus)*modulus + residue
    if strict_lower < lower: strict_lower += modulus
    strict_upper = (upper//modulus)*modulus + residue
    if strict_upper > upper: strict_upper -= modulus
    if order == 'asc':
        return range(strict_lower, strict_upper + 1, modulus)
    elif order == 'desc':
        return range(strict_upper, strict_lower - 1, -modulus)

# Returns true if any consecutive sequence of numbers
# in the desc sorted array adds up to target
def is_consecutive_sum(desc_array, start, end, target):
    #print("desc_array [{0}:{1}] = {2}".format(start, end, desc_array[start:end]))
    if (end - start) <= 1:
        return False
    result = sum(desc_array[start:end])
    if result == target:
        return True
    elif result > target:
        return\
        is_consecutive_sum(desc_array, start, end-1, target)\
        or\
        is_consecutive_sum(desc_array, start+1, end, target)
    else:
        return False

# Checks every congruence class            
def is_palindrome_sum_of_squares(number, difference):
    limit = int(sqrt(number)) #The limit can be optimized?
    for i in range(0, difference):
        AP = congruence_class(i, difference, 1, limit, 'desc')
        squaredAP = list(map(lambda x: x*x, AP))
        if is_consecutive_sum(squaredAP, 0, len(squaredAP), number):
            return True

# Generator to yield palindromes 
def generate_palindromes(start, stop, step = 1):
    for x in range(start, stop, step):
        if str(x) == str(x)[::-1]:
            yield x

# What the problem actually requires
def sum_of_desired_palindromes(number, difference):
    palindrome_sums = 0
    for i in generate_palindromes(1, number+1):
        if is_palindrome_sum_of_squares(i, difference):
            palindrome_sums += i
    return palindrome_sums
        
if __name__ == "__main__":
    print(sum_of_desired_palindromes(10, 1))