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 1.8.0) (judge verdict: Accepted)

/*****Author: Satyajeet Singh************************************/
    import java.io.*;
    import java.util.*;
    import java.text.*; 
    import java.lang.*;
    import java.math.*;
public class Main{
/*********************************************Constants******************************************/
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));        
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static long mod=(long)1e9+7;
    static long mod1=998244353;
    static ArrayList<Integer> graph[];
    static int pptr=0,pptrmax=0;
    static String st[];
/*****************************************Solution Begins***************************************/    
    
    public static void main(String args[]) throws Exception{
        int n=pi();
        int k=pi();
        int input[]=new int[n];
        for(int i=0;i<n;i++){
            input[i]=pi();
        }
        long start=1;
        long end=(long)1e9;
        long ans=0;
        while(start<=end){
            long mid=(start+end)/2;
            long tt=0;
            for(int u:input){
                long ops=u/mid;
                if(u%mid==0)ops--;
                tt+=ops;
            }
            if(tt<=k){
                end=mid-1;
                ans=mid;
            }           
            else{
                start=mid+1;
            } 
        }
        out.println(ans);
/****************************************Solution Ends**************************************************/
        clr();
    }
    static void clr(){
        out.flush();
        out.close();
    }
    static void nl() throws Exception{
        pptr=0;
        st=br.readLine().split(" ");
        pptrmax=st.length;
    }
    static void nls() throws Exception{
        pptr=0;
        st=br.readLine().split("");
        pptrmax=st.length;
    }
    static int pi() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Integer.parseInt(st[pptr++]);
    }
    static long pl() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Long.parseLong(st[pptr++]);
    }
    static double pd() throws Exception{
        if(pptr==pptrmax)
            nl();
        return Double.parseDouble(st[pptr++]);
    }
    static String ps() throws Exception{
        if(pptr==pptrmax)
            nl();
        return st[pptr++];
    }
/***************************************Precision Printing**********************************************/
    static void printPrecision(double d){
        DecimalFormat ft = new DecimalFormat("0.00000000000"); 
        out.println(ft.format(d));
    }
/**************************************Bit Manipulation**************************************************/
    static int countBit(long mask){
        int ans=0;
        while(mask!=0){
            mask&=(mask-1);
            ans++;
        }
        return ans;
    }
/******************************************Graph*********************************************************/
    static void Makegraph(int n){
        graph=new ArrayList[n];
        for(int i=0;i<n;i++)
            graph[i]=new ArrayList<>();
    }
    static void addEdge(int a,int b){
        graph[a].add(b);
    }
    // static void addEdge(int a,int b,int c){
    //     graph[a].add(new Pair(b,c));
    // }    
/*********************************************PAIR********************************************************/
    static class Pair{
        int u;
        int v;
        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/******************************************Long Pair*******************************************************/
    static class Pairl{
        long u;
        long v;
        public Pairl(long u, long v) {
            this.u = u;
            this.v = v;
        }
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
        public boolean equals(Object o) {
            Pairl other = (Pairl) o;
            return u == other.u && v == other.v;
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/*****************************************DEBUG***********************************************************/
    public static void debug(Object... o){
        System.out.println(Arrays.deepToString(o));
    }
/************************************MODULAR EXPONENTIATION***********************************************/
    static long modulo(long a,long b,long c){
        long x=1,y=a%c;
        while(b > 0){
            if(b%2 == 1)
                x=(x*y)%c;
            y = (y*y)%c;
            b = b>>1;
        }
        return  x%c;
    }
/********************************************GCD**********************************************************/
    static long gcd(long x, long y){
        if(x==0)
            return y;
        if(y==0)
            return x;
        long r=0, a, b;
        a = (x > y) ? x : y; 
        b = (x < y) ? x : y;
        r = b;
        while(a % b != 0){
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }
}