Problem:
Max Score: 350 Points

Problem Statement

There are N buildings along the line. The i-th building from the left is colored in color i, and its height is currently a_i meters.

Chokudai is a mayor of the city, and he loves colorful thigs. And now he wants to see at least K buildings from the left.

You can increase height of buildings, but it costs 1 yens to increase 1 meters. It means you cannot make building that height is not integer.

You cannot decrease height of buildings.

Calculate the minimum cost of satisfying Chokudai's objective.

Note: "Building i can see from the left" means there are no j exists that (height of building j) ≥ (height of building i) and j < i.

Input Format

N K
a_1 a_2 a_3 ... a_N

Output Format

Print the minimum cost in one line. In the end put a line break.

Constraints

1 ≤ K ≤ N ≤ 15

1 ≤ a_i ≤ 10^9

Scoring

Subtask 1 [120 points]

N = K

Subtask 2 [90 points]

N ≤ 5

a_i ≤ 7

Subtask 3 [140 points]

There are no additional constraints.

Sample Input 1

5 5
3949 3774 3598 3469 3424

Sample Output 1

1541

The optimal solution is (height of buildings from the left) = [3949, 3950, 3951, 3952, 3953].

Sample Input 2

5 3
7 4 2 6 4

Sample Output 2

7

The optimal solution is (height of buildings from the left) = [7, 8, 2, 9, 4].

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

//#include <bits/stdc++.h>
//#include <stdio.h>
#include<iostream>
#include<cstdio>
#include<bitset>
#include<algorithm>
#include<vector>
#include<list>
#include<queue>
#include<stack>
#include<string>
#include<string.h>
#include<cmath>
#include<utility>
#include<functional>
#include<map>
#include<set>
#include<cctype>
#include<fstream>


#define FOR(i, a, b) for( int i=(a);i<=(b);i++)
#define RFOR(i, a, b) for( int i=(a);i>=(b);i--)
#define LFOR(i, a, b) for( long long int i=(a);i<=(b);i++)
#define LRFOR(i, a, b) for(long long int i=(a);i>=(b);i--)
#define MOD 1000000007
#define INF 1000000000 //2000000000
#define LLINF 1000000000000000000 //9000000000000000000
#define PI 3.14159265358979
#define MAXI 7500000

using namespace std;
typedef long long int ll;
typedef pair< long long int, long long  int> P;
typedef string::const_iterator State;

int dy[5] = { 0,0,1,-1,0 };
int dx[5] = { 1,-1,0,0 ,0 };


int main(void) {

	ll k, n;
	ll a[16];
	ll total = LLINF;
	ll point = 0;
	ll high = 0;
	ll count = 0;
	bool flag = false;

	cin >> n >> k;
	FOR(i, 0, n-1) {
		cin >> a[i];
	}

	bitset<15> bit;

	FOR(i, 0, pow(2, n) - 1) {
		bit = i;
		//cout << bit << endl;
		count = 0;
		if (bit[0] == false) {
			continue;
		}
		FOR(j, 0, 14) {
			if (bit[j] == true) {
				count++;
			}
		}
		if (count < k) {
			continue;
		}

		point = 0;
		flag = false;
		high = 0;
		FOR(j, 0, 14) {
			if (bit[j] == true) {
				if (a[j] > high) {
					high = a[j];
				}
				else {
					point += high - a[j] + 1;
					high++;
				}
			}
		}

		//cout << i << " " << point << endl;
		if (point < total) {
			total = point;
		}

	}

	cout << total << endl;

	return 0;
}