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.

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.

Input Format


N K
a_1 a_2 a_3 ... a_N

Example

Input

5 5
3949 3774 3598 3469 3424


Output

1541
#include<stdio.h>
#include<limits.h>
#define ll long long
ll a[20],cost=0,ans=LLONG_MAX,k,n,i;
ll min1(ll a,ll b){
	if(a<b)
		return a;
	else
		return b;
}
void match(ll b,ll s,ll e){
	if(b==n){
		if(s>=k){
			ans=min1(ans,cost);
		}
		return ;
	}
	if(a[b]>e){
		match(b+1,s+1,a[b]);
	}
	else{
		match(b+1,s,e);
		cost+=(e+1-a[b]);
		match(b+1,s+1,e+1);
		cost-=(e+1-a[b]);
	}
}
int main(){
	scanf("%lld%lld",&n,&k);
	for(i=0;i<n;i++)
		scanf("%lld",&a[i]);
	match(1,1,a[0]);
	printf("%lld\n",ans);
	return 0;
} 