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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
const ll mod = 1e9+7;
const ll mod1 = 998244353;
const ll inf = 9e18+5;
const double pi = acosl(-1.0l);
#define rep(i,a,b) for(ll i=a;i<b;i++)
const long double eps = 1e-9;

bool equalTo ( double a, double b ){ if ( fabs ( a - b ) <= eps ) return true; else return false; }
bool notEqual ( double a, double b ){if ( fabs ( a - b ) > eps ) return true; else return false; }
bool lessThan ( double a, double b ){ if ( a + eps < b ) return true; else return false; }
bool lessThanEqual ( double a, double b ){if ( a < b + eps ) return true;   else return false;}
bool greaterThan ( double a, double b ){if ( a > b + eps ) return true;else return false;}
bool greaterThanEqual ( double a, double b ){if ( a + eps > b ) return true;else return false;}

void swap(ll &a , ll &b){
    ll t = a;
    a = b;
    b = t;
}

ll min(ll a, ll b){
    if(a<b)return a;
    return b;
}

ll max(ll a, ll b){
    if(a>b)return a;
    return b;
}

 ll pow(ll a, ll b) {
    a %= mod;
    ll ans = 1;
    while (b > 0) {
        if (b & 1)
            ans = ans * a % mod;
        a = a * a % mod;
        b /= 2;
    }
    return ans;
}


//*********Debugger template starts***********************//
#ifndef ONLINE_JUDGE
vector<string> vec_splitter(string s) {
	s += ',';
	vector<string> res;
	while(!s.empty()) {
		res.push_back(s.substr(0, s.find(',')));
		s = s.substr(s.find(',') + 1);
	}
	return res;
}
void debug_out(
vector<string> __attribute__ ((unused)) args,
__attribute__ ((unused)) int idx,
__attribute__ ((unused)) int LINE_NUM) { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(vector<string> args, int idx, int LINE_NUM, Head H, Tail... T) {

	if(idx == 0) {
        cerr << "Line(" << LINE_NUM << ") ";
	}
	stringstream ss; ss << H;
	cerr << " [" << args[idx] << " = " << ss.str() <<"] ";
	debug_out(args, idx + 1, LINE_NUM, T...);

}
#define debug(...) debug_out(vec_splitter(#__VA_ARGS__), 0, __LINE__, __VA_ARGS__)
#else
#define debug(...)
#endif

#ifndef ONLINE_JUDGE
#define n_l '\n'
#define dbg(...) cerr <<"Line("<<__LINE__<<") " "[" << #__VA_ARGS__ << "]: "; cerr << to_string(__VA_ARGS__) << endl
template <typename T, size_t N> int SIZE(const T (&t)[N]){ return N; } template<typename T> int SIZE(const T &t){ return t.size(); } string to_string(const string s, int x1=0, int x2=1e9){ return '"' + ((x1 < s.size()) ? s.substr(x1, x2-x1+1) : "") + '"'; } string to_string(const char* s) { return to_string((string) s); } string to_string(const bool b) { return (b ? "true" : "false"); } string to_string(const char c){ return string({c}); } template<size_t N> string to_string(const bitset<N> &b, int x1=0, int x2=1e9){ string t = ""; for(int __iii__ = min(x1,SIZE(b)),  __jjj__ = min(x2, SIZE(b)-1); __iii__ <= __jjj__; ++__iii__){ t += b[__iii__] + '0'; } return '"' + t + '"'; } template <typename A, typename... C> string to_string(const A (&v), int x1=0, int x2=1e9, C... coords); int l_v_l_v_l = 0, t_a_b_s = 0; template <typename A, typename B> string to_string(const pair<A, B> &p) { l_v_l_v_l++; string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")"; l_v_l_v_l--; return res; } template <typename A, typename... C> string to_string(const A (&v), int x1, int x2, C... coords) { int rnk = rank<A>::value; string tab(t_a_b_s, ' '); string res = ""; bool first = true; if(l_v_l_v_l == 0) res += n_l; res += tab + "["; x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v)); auto l = begin(v); advance(l, x1); auto r = l; advance(r, (x2-x1) + (x2 < SIZE(v))); for (auto e = l; e != r; e = next(e)) { if (!first) { res += ", "; } first = false; l_v_l_v_l++; if(e != l){ if(rnk > 1) { res += n_l; t_a_b_s = l_v_l_v_l; }; } else{ t_a_b_s = 0; } res += to_string(*e, coords...); l_v_l_v_l--; } res += "]"; if(l_v_l_v_l == 0) res += n_l; return res; } void dbgm(){;} template<typename Heads, typename... Tails> void dbgm(Heads H, Tails... T){ cerr << to_string(H) << " | "; dbgm(T...); }
#else
    #define dbg(...)
#endif
//*********Debugger template ends ***********************//

ll n;
const int mx = 2e5+3;
ll a[mx];
ll k;
bool ok(ll len){

  ll cnt = 0;

  for(int i = 0 ; i < n;i++){
    if(a[i] == len)continue;
    cnt += a[i]/len;
    if(cnt > k )return false;
  }
  if(cnt <=k){
    return true;
  }
  return false;
}


int main()
{


    ios_base :: sync_with_stdio(0);
    cin.tie(0);


    cin>>n>>k;
    rep(i ,0 , n){
        cin>>a[i];
    }
    ll st = 1 , en = 1e9;
    ll ans = -1;
    while(st<=en){
        ll mid = st+en;
        mid /= 2;
        if(ok(mid)){
            ans = mid;
            en = mid-1;
        }
        else
            st = mid+1;

    }
    cout<<ans;

}