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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <limits.h>
int max(int a, int b){return a>b?a:b;}
int min(int a, int b){return a<b?a:b;}
int gcd(int a, int b){return min(a,b)==0 ?max(a,b):gcd(min(a,b),max(a,b)%min(a,b));}
long long llmax(long long a, long long b){return a>b?a:b;}
long long llmin(long long a, long long b){return a<b?a:b;}
long long llgcd(long long a, long long b){return min(a,b)==0 ?max(a,b):gcd(min(a,b),max(a,b)%min(a,b));}
int assort(const void *a, const void *b){return *(int*)a-*(int*)b;}
int dessort(const void *a, const void *b){return *(int*)b-*(int*)a;}
int llassort(const void *a, const void *b){return *(long long*)a-*(long long*)b;}
int lldessort(const void *a, const void *b){return *(long long*)b-*(long long*)a;}
int charassort(const void *a, const void *b){return strcmp((char*)a ,(char*)b);}
int chardessort(const void *a, const void *b){return strcmp((char*)b ,(char*)a);}
char lowcmp[26]="abcdefghijklmnopqrstuvwxyz";
char upcmp[26]="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
int ntoi(char c){return c-'0';}
int ltoi(char c){return c-'a';}
int utoi(char c){return c-'A';}
long long mod=1000000007;

int main(void){
    int n,k,ans=0;
    scanf("%d%d",&n,&k);
    int a[n];
    for (int i=0; i<n; i++){
        scanf("%d",&a[i]);
    }
    while(1){
        int count=1,tmp=a[0],build;
        for (int i=0; i<n; i++){
            if (tmp<a[i]){
                count++;
                tmp=a[i];
            }
        }
        if (count<k){
            count=a[0],tmp=1e9,build=0;
            for (int i=1; i<n; i++){
                if (a[i]<=count && tmp>count-a[i]){
                    tmp=count-a[i];
                    build=i;
                } else if (a[i]>=count) {
                    count=a[i];
                }
                
            }
            a[build]+=tmp+1;
            ans+=tmp+1;
        } else {
            break;
        }
    }
    printf("%d\n",ans);
	return 0 ;
}