1.2 KB | 1199 chars
"""
[14565: 역원(Inverse) 구하기](https://www.acmicpc.net/problem/14565)
Tier: Gold 2
Category: extended_euclidean, math, modular_multiplicative_inverse, number_theory
"""
import sys
from math import sqrt, pi, sin, factorial, ceil, floor
from datetime import datetime, timedelta
SYS_INPUT = True
RECURSION_LIMIT = 10 ** 7
SET_RECURSION = False
BLANK = " "
if SET_RECURSION:
sys.setrecursionlimit(RECURSION_LIMIT)
inp = lambda : sys.stdin.readline().rstrip() if SYS_INPUT else input()
mii = lambda : [*map(int,inp().split())]
mfi = lambda : [*map(float,inp().split())]
ii = lambda : int(inp())
fi = lambda : float(inp())
isplit = lambda : inp().split()
p = print
def gcd(a, b): return gcd(b, a % b) if b > 0 else a
def lcm(a, b): return a * b // gcd(a, b)
def extended_gcd(a, b):
if b == 0:
return a, 1, 0
else:
gcd, x1, y1 = extended_gcd(b, a % b)
x, y = y1, x1 - (a // b) * y1
return gcd, x, y
def mod_inverse(a, mod):
gcd, x, _ = extended_gcd(a, mod)
if gcd != 1:
return -1
return x % mod
def solve():
N, A = mii()
print(N - A, mod_inverse(A, N))
if __name__ == "__main__":
tc = 1
for t in range(1, tc+1):
ret = solve()