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 K[20],cost,ans=LLONG_MAX,a,b,i;
ll min1(ll a,ll b){
	if(a<b)
		return a;
	else
		return b;
}
void match(ll c,ll d,ll e){
	if(c==a){
		if(d>=b){
			ans=min1(ans,cost);
		}
		return ;
	}
	if(K[c]>e){
		match(c+1,d+1,K[c]);
	}
	else{
		match(c+1,d,e);
		cost+=(e+1-K[c]);
		match(c+1,d+1,e+1);
		cost-=(e+1-K[c]);
	}
}
int main(){
	scanf("%lld%lld",&a,&b);
	for(i=0;i<a;i++)
		scanf("%lld",&K[i]);
	match(1,1,K[0]);
	printf("%lld\n",ans);
	return 0;
} 