Problem:
Score : 300 points

Problem Statement

Given any integer x, Aoki can do the operation below.

Operation: Replace x with the absolute difference of x and K.

You are given the initial value of an integer N. Find the minimum possible value taken by N after Aoki does the operation zero or more times.

Constraints

0 ≤ N ≤ 10^{18}

1 ≤ K ≤ 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the minimum possible value taken by N after Aoki does the operation zero or more times.

Sample Input 1

7 4

Sample Output 1

1

Initially, N=7.

After one operation, N becomes |7-4| = 3.

After two operations, N becomes |3-4| = 1, which is the minimum value taken by N.

Sample Input 2

2 6

Sample Output 2

2

N=2 after zero operations is the minimum.

Sample Input 3

1000000000000000000 1

Sample Output 3

0

Solution in Python (3.4.3) (judge verdict: Accepted)

import sys, re, os
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import permutations, combinations, product, accumulate
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from fractions import gcd
 
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def S_MAP(): return map(str, input().split())
def LIST(): return list(map(int, input().split()))
def S_LIST(): return list(map(str, input().split()))
 
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

N, K = MAP()

if N <= K:
    print(min(K-N, N))
# elif K == 1:
#     print(0)
else:
    print(min(N % K, K - N % K))
    # a = N // K
    # b = ceil(N / K)
    # c = N % K
    # print(a, b, c)
    # print(abs(c-K), abs(c))

    # x = N // (N - K)
    # y = x + 1
    # z = x - 1
    # print(x, y, z)
    # a = N - x * (N-K)
    # b = N - y * (N-K)
    # c = N - z * (N-K)
    # print(a, b, c)
    # ans = min(abs(a), abs(b), abs(c))
    # print(ans)

# if N >= K:
#     ans = min(abs(a), abs(b))
# # K > N:
# else:
#     ans = min(K-N, N)
# print(ans)