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"""

Extended Euclidean Algorithm.

Finds 2 numbers a and b such that it satisfies

the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)

"""

# @Author: S. Sharma <silentcat>

# @Date: 2019-02-25T12:08:53-06:00

# @Email: silentcat@protonmail.com

# @Last modified by: PatOnTheBack

# @Last modified time: 2019-07-05

import sys

def extended_euclidean_algorithm(m, n):

"""

Extended Euclidean Algorithm.

Finds 2 numbers a and b such that it satisfies

the equation am + bn = gcd(m, n) (a.k.a Bezout's Identity)

"""

a = 0

a_prime = 1

b = 1

b_prime = 0

q = 0

r = 0

if m > n:

c = m

d = n

else:

c = n

d = m

while True:

q = int(c / d)

r = c % d

if r == 0:

break

c = d

d = r

t = a_prime

a_prime = a

a = t - q * a

t = b_prime

b_prime = b

b = t - q * b

pair = None

if m > n:

pair = (a, b)

else:

pair = (b, a)

return pair

def main():

"""Call Extended Euclidean Algorithm."""

if len(sys.argv) < 3:

print("2 integer arguments required")

exit(1)

m = int(sys.argv[1])

n = int(sys.argv[2])

print(extended_euclidean_algorithm(m, n))

if __name__ == "__main__":

main()

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