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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"errors"
	"fmt"
	"io"
	"math"
	"os"
	"strconv"
)

/*********** I/O ***********/

var (
	// ReadString returns a WORD string.
	ReadString func() string
	stdout     *bufio.Writer
)

func newReadString(ior io.Reader, sf bufio.SplitFunc) func() string {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+9)) // for Codeforces
	r.Split(sf)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

// ReadInt returns an integer.
func ReadInt() int {
	return int(readInt64())
}
func ReadInt2() (int, int) {
	return int(readInt64()), int(readInt64())
}
func ReadInt3() (int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64())
}
func ReadInt4() (int, int, int, int) {
	return int(readInt64()), int(readInt64()), int(readInt64()), int(readInt64())
}

// ReadInt64 returns as integer as int64.
func ReadInt64() int64 {
	return readInt64()
}
func ReadInt64_2() (int64, int64) {
	return readInt64(), readInt64()
}
func ReadInt64_3() (int64, int64, int64) {
	return readInt64(), readInt64(), readInt64()
}
func ReadInt64_4() (int64, int64, int64, int64) {
	return readInt64(), readInt64(), readInt64(), readInt64()
}

func readInt64() int64 {
	i, err := strconv.ParseInt(ReadString(), 0, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

// ReadIntSlice returns an integer slice that has n integers.
func ReadIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt()
	}
	return b
}

// ReadInt64Slice returns as int64 slice that has n integers.
func ReadInt64Slice(n int) []int64 {
	b := make([]int64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadInt64()
	}
	return b
}

// ReadFloat64 returns an float64.
func ReadFloat64() float64 {
	return float64(readFloat64())
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(ReadString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

// ReadFloatSlice returns an float64 slice that has n float64.
func ReadFloat64Slice(n int) []float64 {
	b := make([]float64, n)
	for i := 0; i < n; i++ {
		b[i] = ReadFloat64()
	}
	return b
}

// ReadRuneSlice returns a rune slice.
func ReadRuneSlice() []rune {
	return []rune(ReadString())
}

/*********** Debugging ***********/

// ZeroPaddingRuneSlice returns binary expressions of integer n with zero padding.
// For debugging use.
func ZeroPaddingRuneSlice(n, digitsNum int) []rune {
	sn := fmt.Sprintf("%b", n)

	residualLength := digitsNum - len(sn)
	if residualLength <= 0 {
		return []rune(sn)
	}

	zeros := make([]rune, residualLength)
	for i := 0; i < len(zeros); i++ {
		zeros[i] = '0'
	}

	res := []rune{}
	res = append(res, zeros...)
	res = append(res, []rune(sn)...)

	return res
}

// Strtoi is a wrapper of strconv.Atoi().
// If strconv.Atoi() returns an error, Strtoi calls panic.
func Strtoi(s string) int {
	if i, err := strconv.Atoi(s); err != nil {
		panic(errors.New("[argument error]: Strtoi only accepts integer string"))
	} else {
		return i
	}
}

// PrintIntsLine returns integers string delimited by a space.
func PrintIntsLine(A ...int) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.Itoa(A[i])
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintIntsLine returns integers string delimited by a space.
func PrintInts64Line(A ...int64) string {
	res := []rune{}

	for i := 0; i < len(A); i++ {
		str := strconv.FormatInt(A[i], 10) // 64bit int version
		res = append(res, []rune(str)...)

		if i != len(A)-1 {
			res = append(res, ' ')
		}
	}

	return string(res)
}

// PrintfDebug is wrapper of fmt.Fprintf(os.Stderr, format, a...)
func PrintfDebug(format string, a ...interface{}) {
	fmt.Fprintf(os.Stderr, format, a...)
}

// PrintfBufStdout is function for output strings to buffered os.Stdout.
// You may have to call stdout.Flush() finally.
func PrintfBufStdout(format string, a ...interface{}) {
	fmt.Fprintf(stdout, format, a...)
}

/********** FAU standard libraries **********/

//fmt.Sprintf("%b\n", 255) 	// binary expression

/********** I/O usage **********/

//str := ReadString()
//i := ReadInt()
//X := ReadIntSlice(n)
//S := ReadRuneSlice()
//a := ReadFloat64()
//A := ReadFloat64Slice(n)

//str := ZeroPaddingRuneSlice(num, 32)
//str := PrintIntsLine(X...)

/*
ASCII code

ASCII   10進数  ASCII   10進数  ASCII   10進数
!       33      "       34      #       35
$       36      %       37      &       38
'       39      (       40      )       41
*       42      +       43      ,       44
-       45      .       46      /       47
0       48      1       49      2       50
3       51      4       52      5       53
6       54      7       55      8       56
9       57      :       58      ;       59
<       60      =       61      >       62
?       63      @       64      A       65
B       66      C       67      D       68
E       69      F       70      G       71
H       72      I       73      J       74
K       75      L       76      M       77
N       78      O       79      P       80
Q       81      R       82      S       83
T       84      U       85      V       86
W       87      X       88      Y       89
Z       90      [       91      \       92
]       93      ^       94      _       95
`       96      a       97      b       98
c       99      d       100     e       101
f       102     g       103     h       104
i       105     j       106     k       107
l       108     m       109     n       110
o       111     p       112     q       113
r       114     s       115     t       116
u       117     v       118     w       119
x       120     y       121     z       122
{       123     |       124     }       125
~       126             127
*/

/*******************************************************************/

const (
	// General purpose
	MOD          = 1000000000 + 7
	ALPHABET_NUM = 26
	INF_INT64    = math.MaxInt64
	INF_BIT60    = 1 << 60
	INF_INT32    = math.MaxInt32
	INF_BIT30    = 1 << 30
	NIL          = -1

	// for dijkstra, prim, and so on
	WHITE = 0
	GRAY  = 1
	BLACK = 2
)

func init() {
	ReadString = newReadString(os.Stdin, bufio.ScanWords)
	stdout = bufio.NewWriter(os.Stdout)
}

var (
	n, k int
)

// func main() {
// 	n, k = ReadInt2()

// 	if n == 0 || k == 1 || n == k || n%k == 0 {
// 		fmt.Println(0)
// 		return
// 	}

// 	ans := Gcd(n, k)
// 	// fmt.Println(ans)
// 	fmt.Println(Min(ans, n))
// }

func main() {
	n, k = ReadInt2()

	if n == 0 || k == 1 || n%k == 0 {
		fmt.Println(0)
		return
	}

	r := n % k
	ir := k - r

	// if r == 0 || ir == 0 || r == 1 || ir == 1 {
	// 	fmt.Println(0)
	// 	return
	// }
	fmt.Println(Min(r, ir))

	// fmt.Println(Min(Gcd(r, k), Gcd(ir, k)))
}

// Min returns the min integer among input set.
// This function needs at least 1 argument (no argument causes panic).
func Min(integers ...int) int {
	m := integers[0]
	for i, integer := range integers {
		if i == 0 {
			continue
		}
		if m > integer {
			m = integer
		}
	}
	return m
}

// Gcd returns the Greatest Common Divisor of two natural numbers.
// Gcd only accepts two natural numbers (a, b >= 1).
// 0 or negative number causes panic.
// Gcd uses the Euclidean Algorithm.
func Gcd(a, b int) int {
	if a <= 0 || b <= 0 {
		panic(errors.New("[argument error]: Gcd only accepts two NATURAL numbers"))
	}
	if a < b {
		a, b = b, a
	}

	// Euclidean Algorithm
	for b > 0 {
		div := a % b
		a, b = b, div
	}

	return a
}

// Lcm returns the Least Common Multiple of two natural numbers.
// Lcd only accepts two natural numbers (a, b >= 1).
// 0 or negative number causes panic.
// Lcd uses the Euclidean Algorithm indirectly.
func Lcm(a, b int) int {
	if a <= 0 || b <= 0 {
		panic(errors.New("[argument error]: Gcd only accepts two NATURAL numbers"))
	}

	// a = a'*gcd, b = b'*gcd, a*b = a'*b'*gcd^2
	// a' and b' are relatively prime numbers
	// gcd consists of prime numbers, that are included in a and b
	gcd := Gcd(a, b)

	// not (a * b / gcd), because of reducing a probability of overflow
	return (a / gcd) * b
}

/*
- まずは全探索を検討しましょう
- MODは最後にとりましたか？
- 負のMODはちゃんと関数を使って処理していますか？
- ループを抜けた後も処理が必要じゃありませんか？
- 和・積・あまりを求められたらint64が必要ではありませんか？
- いきなりオーバーフローはしていませんか？
- MOD取る系はint64必須ですよ？
- 後ろ・逆・ゴールから考えましたか？
- 3者のうち真ん中に着目しましたか？
*/

/*******************************************************************/