Problem:
Score : 500 points

Problem Statement

We have N logs of lengths A_1,A_2,\cdots A_N.

We can cut these logs at most K times in total. When a log of length L is cut at a point whose distance from an end of the log is t (0<t<L), it becomes two logs of lengths t and L-t.

Find the shortest possible length of the longest log after at most K cuts, and print it after rounding up to an integer.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq K \leq 10^9

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \cdots A_N

Output

Print an integer representing the answer.

Sample Input 1

2 3
7 9

Sample Output 1

4

First, we will cut the log of length 7 at a point whose distance from an end of the log is 3.5, resulting in two logs of length 3.5 each.

Next, we will cut the log of length 9 at a point whose distance from an end of the log is 3, resulting in two logs of length 3 and 6.

Lastly, we will cut the log of length 6 at a point whose distance from an end of the log is 3.3, resulting in two logs of length 3.3 and 2.7.

In this case, the longest length of a log will be 3.5, which is the shortest possible result. After rounding up to an integer, the output should be 4.

Sample Input 2

3 0
3 4 5

Sample Output 2

5

Sample Input 3

10 10
158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202

Sample Output 3

292638192

Solution in Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"sort"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)
var out = bufio.NewWriter(os.Stdout)

func main() {
	/*/TODO:!!!!!!!テスト用!!!!!!!!!
	sc = bufio.NewScanner(strings.NewReader(`
										`))
	//TODO:!!!!!!!テスト用!!!!!!!!!*/

	buf := make([]byte, 1024*1024)
	sc.Buffer(buf, bufio.MaxScanTokenSize)
	sc.Split(bufio.ScanWords)
	defer out.Flush() // !!!!caution!!!! you must use Fprint(out, ) not Print()
	/* --- code --- */
	//fmt.Fprintln(out, "[DEBUG]", time.Now())

	n := nextInt()
	k := nextInt()

	a := make([]int, n)
	sum := 0

	for i := 0; i < n; i++ {
		a[i] = nextInt()
		sum += a[i]
	}

	ans := divCeil(sum, (n + k))

	for i := 0; i < 10000; i++ {
		wk := 0
		na := ans * 2

		for j := 0; j < n; j++ {
			d := divCeil(a[j], ans)
			wk += d
			if d > 1 {
				na = minInt(na, divCeil(a[j], d-1))
			}
		}
		//		fmt.Fprintln(out, "[DEBUG]", wk, ans, na)
		if wk <= n+k {
			break
		}
		ans = na
	}

	//fmt.Fprintln(out, "[DEBUG]", a)
	fmt.Fprintln(out, ans)

}

// 挿入ソート配列
type slist struct {
	l []int
}

func makeSlist() slist {
	return slist{[]int{}}
}

func (s *slist) add(a int) {
	pos := sort.Search(len(s.l), func(i int) bool { return s.l[i] >= a })
	if pos < len(s.l) {
		s.l = append(s.l[:pos+1], s.l[pos:]...)
		s.l[pos] = a
	} else {
		s.l = append(s.l, a)
	}
}
func (s slist) contains(a int) bool {
	pos := sort.Search(len(s.l), func(i int) bool { return s.l[i] >= a })
	return pos < len(s.l) && s.l[pos] == a
}

//------------------------------------------------------------------------------

// -*-*-*-*-*-*-*-*-
// * I/O utilities *
// -*-*-*-*-*-*-*-*-

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}

func nextFloat64() float64 {
	a, _ := strconv.ParseFloat(next(), 64)
	return a
}

func nextInts(n int) []int {
	ret := make([]int, n)
	for i := 0; i < n; i++ {
		ret[i] = nextInt()
	}
	return ret
}
func nextFloats(n int) []float64 {
	ret := make([]float64, n)
	for i := 0; i < n; i++ {
		ret[i] = nextFloat64()
	}
	return ret
}
func nextStrings(n int) []string {
	ret := make([]string, n)
	for i := 0; i < n; i++ {
		ret[i] = next()
	}
	return ret
}

func chars(s string) []string {
	ret := make([]string, len([]rune(s)))
	for i, v := range []rune(s) {
		ret[i] = string(v)
	}
	return ret
}

func printArray(a []int) {
	for i := 0; i < len(a); i++ {
		if i >= 1 {
			fmt.Fprint(out, " ")
		}
		fmt.Fprint(out, a[i])
	}
	fmt.Fprintln(out)
}

func absInt(x int) int {
	return int(math.Abs(float64(x)))
}
func minInt(x, y int) int {
	if x < y {
		return x
	}
	return y
}
func maxInt(x, y int) int {
	if x > y {
		return x
	}
	return y
}
func log10(x int) float64 {
	return math.Log10(float64(x))
}
func divCeil(shi, bo int) int {
	ans := shi / bo
	if shi%bo != 0 {
		ans++
	}
	return ans
}