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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Arrays;
import java.util.Scanner;


public class Main {

    public static String Y = "Yes";
    public static String N = "No";
    public static long MOD = (long) (Math.pow(10, 9) + 7);
    public static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {

        int n = ni();
        long k = nl();

        long[] a = new long[n];
        long start = 0;
        long last = -1;
        for (int i = 0; i < n; i++) {
            a[i] = nl();
            if (last < a[i]) {
                last = a[i];
            }
        }
        last++;

        // 二分探索（X以下に出来るかどうか）
        while (last - start > 1) {

            long now = (last + start) / 2;
            if (!canSolve(now, a, k)) {
                start = now;
            } else {
                last = now;
            }
        }
        out(last);
    }

    static boolean canSolve(long len, long[] a, long k) {

        /*
         * k回以下の伐採ですべてをx以下にできるか
         */
        boolean flg = false;
        long count = 0; // 切る回数
        for (int i = 0; i < a.length; i++) {
            count += (long) Math.ceil((double) a[i] / (double) len) - 1;
            // debug(len + " " + count + " " + Math.ceil((double) a[i] / (double) len));
        }

        if (count <= k) {
            flg = true;
        } else {
            flg = false;
        }

        return flg;
    }

    /*
     * 以下メソッド集
     */
    static char[][] same(char[][] c, int h, int w) {

        char[][] a = new char[h][w];
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                a[i][j] = c[i][j];
            }
        }
        return a;

    }

    static int countkuro(char[][] c) {

        int count = 0;
        for (char[] cc : c) {
            for (char ccc : cc) {
                if ('#' == ccc) {
                    count++;
                }
            }
        }
        return count;
    }

    static double[] sort(double[] r) {

        Arrays.sort(r);
        return r;
    }

    static void debug() {

        out("---");
    }

    static void debug(long a) {

        out("-------");
        out(a);
        out("-------");
    }

    static void debug(double a) {

        out("-------");
        out(a);
        out("-------");
    }

    static void debug(String a) {

        out("-------");
        out(a);
        out("-------");
    }

    static long[] sort(long[] n) {

        Arrays.sort(n);
        return n;
    }

    static int ketasuu(int n) {

        String str = "" + n;
        return str.length();
    }

    static int account(String str) {

        String target = "AC";
        int count = 0;
        int len = str.length();
        for (int i = 0; i < len - 1; i++) {
            if (target.equals(str.substring(i, i + target.length()))) {
                count++;
            }
        }
        return count;
    }

    static int ni() {

        return sc.nextInt();
    }

    static long nl() {

        return sc.nextLong();
    }

    static double nd() {

        return sc.nextDouble();
    }

    static String n() {

        return sc.next();
    }

    static char[] nc() {

        return sc.next().toCharArray();
    }

    static int kaijo(int n) {

        if (n == 0 || n == 1) {
            return 1;
        } else {
            return n * kaijo(n - 1);
        }
    }

    static int fib(int n) {

        return (n == 1 || n == 0) ? n : fib(n - 2) + fib(n - 1);
    }

    static long lcm(long m, long n) {

        return m * n / gcd(m, n);
    }

    static int lcm(int m, int n) {

        return m * n / gcd(m, n);
    }

    static long gcd(long a, long b) {

        return (b == 0) ? a : gcd(b, a % b);
    }

    static int gcd(int a, int b) {

        return (b == 0) ? a : gcd(b, a % b);
    }

    static void out(String info) {

        System.out.println(info);
    }

    static void out(int info) {

        System.out.println(info);
    }

    static void out(double info) {

        System.out.println(info);
    }

    static void out(long info) {

        System.out.println(info);
    }

    static void out(char info) {

        System.out.println(info);
    }

    static void out(Object obj) {

        System.out.println(obj.toString());
    }

    static void outn(String info) {

        System.out.print(info);
    }

    static void outn(int info) {

        System.out.print(info);
    }

    static void outn(double info) {

        System.out.print(info);
    }

    static void outn(long info) {

        System.out.print(info);
    }

    static void outn(char info) {

        System.out.print(info);
    }

    static double max(double d, double e) {

        return Math.max(d, e);
    }

    static long max(long a, long b) {

        return Math.max(a, b);
    }

    static long min(long d, long e) {

        return Math.min(d, e);
    }

    static int min(int a, int b) {

        return Math.min(a, b);
    }
}


class XY {

    int h;
    int c;

    XY(int h, int c) {
        this.h = h;
        this.c = c;
    }
}