Algorithm

D. Cutting Out
time limit per test
3 seconds
memory limit per test
256 megabytes
Problem link- https://codeforces.com/contest/1077/problem/D
input
standard input
output
standard output

You are given an array s� consisting of n� integers.

You have to find any array t� of length k� such that you can cut out maximum number of copies of array t� from array s�.

Cutting out the copy of t� means that for each element ti�� of array t� you have to find ti�� in s� and remove it from s�. If for some ti�� you cannot find such element in s�, then you cannot cut out one more copy of t�. The both arrays can contain duplicate elements.

For example, if s=[1,2,3,2,4,3,1]�=[1,2,3,2,4,3,1] and k=3�=3 then one of the possible answers is t=[1,2,3]�=[1,2,3]. This array t� can be cut out 22 times.

  • To cut out the first copy of t� you can use the elements [1,2––,3,2,4,3––,1––][1,2_,3,2,4,3_,1_] (use the highlighted elements). After cutting out the first copy of t� the array s� can look like [1,3,2,4][1,3,2,4].
  • To cut out the second copy of t� you can use the elements [1––,3––,2––,4][1_,3_,2_,4]. After cutting out the second copy of t� the array s� will be [4][4].

Your task is to find such array t� that you can cut out the copy of t� from s� maximum number of times. If there are multiple answers, you may choose any of them.

Input

The first line of the input contains two integers n� and k� (1≤k≤n≤2⋅1051≤�≤�≤2⋅105) — the number of elements in s� and the desired number of elements in t�, respectively.

The second line of the input contains exactly n� integers s1,s2,…,sn�1,�2,…,�� (1≤si≤2⋅1051≤��≤2⋅105).

Output

Print k� integers — the elements of array t� such that you can cut out maximum possible number of copies of this array from s�. If there are multiple answers, print any of them. The required array t� can contain duplicate elements. All the elements of t� (t1,t2,…,tk�1,�2,…,��) should satisfy the following condition: 1≤ti≤2⋅1051≤��≤2⋅105.

Examples
input
Copy
7 3
1 2 3 2 4 3 1
output
Copy
1 2 3
input
Copy
10 4
1 3 1 3 10 3 7 7 12 3
output
Copy
7 3 1 3
input
Copy
15 2
1 2 1 1 1 2 1 1 2 1 2 1 1 1 1
output
Copy
1 1
Note

The first example is described in the problem statement.

In the second example the only answer is [7,3,1,3][7,3,1,3] and any its permutations. It can be shown that you cannot choose any other array such that the maximum number of copies you can cut out would be equal to 22.

In the third example the array t� can be cut out 55 times.

 



 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include <bits/stdc++.h>

using namespace std;

int const N = 4e5 + 10;
int n, k, a[N];
pair<int, int> fr[N];

bool can(int mid) {
  int with = 0;
  for(int i = 0; i < N; ++i)
    if(with >= k)
      return true;
    else
      with += fr[i].first / mid;
  return with >= k;
}

int main() {
  for(int i = 0; i < N; ++i)
    fr[i].second = i;

  scanf("%d %d", &n, &k);
  for(int i = 0; i < n; ++i)
    scanf("%d", a + i), ++fr[a[i]].first;

  sort(fr, fr + N);
  reverse(fr, fr + N);

  int l = 1, r = 1e9, res = 0, mid;
  while(l <= r) {
    mid = (l + r) >> 1;
    if(can(mid))
      res = mid, l = mid + 1;
    else
      r = mid - 1;
  }

  int cnt = 0;
  for(int i = 0; cnt < k && i < N; ++i) {
    for(int j = 0, to = fr[i].first / res; cnt < k && j < to; ++j)
      printf("%d ", fr[i].second), ++cnt;
  }
  puts("");

  return 0;
}
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Input

x
–
+
cmd
7 3
1 2 3 2 4 3 1

Output

x
–
+
cmd
1 2 3
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Codeforces Solution-D. Cutting Out-Solution in C, C++, Java, Python,Cutting Out

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