#include <iostream>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <time.h>
#include <stdlib.h>
#include <string>
#include <bitset>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <algorithm>
#include <sstream>
#include <stack>
#include <iomanip>
using namespace std;
#define pb push_back
#define mp make_pair
typedef pair<int,int> pii;
typedef long long ll;
typedef double ld;
typedef vector<int> vi;
#define fi first
#define se second
#define fe first
#define FO(x) {freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);}
#define Edg int M=0,fst[SZ],vb[SZ],nxt[SZ];void ad_de(int a,int b){++M;nxt[M]=fst[a];fst[a]=M;vb[M]=b;}void adde(int a,int b){ad_de(a,b);ad_de(b,a);}
#define Edgc int M=0,fst[SZ],vb[SZ],nxt[SZ],vc[SZ];void ad_de(int a,int b,int c){++M;nxt[M]=fst[a];fst[a]=M;vb[M]=b;vc[M]=c;}void adde(int a,int b,int c){ad_de(a,b,c);ad_de(b,a,c);}
#define es(x,e) (int e=fst[x];e;e=nxt[e])
#define esb(x,e,b) (int e=fst[x],b=vb[e];e;e=nxt[e],b=vb[e])
#define VIZ {printf("digraph G{\n"); for(int i=1;i<=n;i++) for es(i,e) printf("%d->%d;\n",i,vb[e]); puts("}");}
#define VIZ2 {printf("graph G{\n"); for(int i=1;i<=n;i++) for es(i,e) if(vb[e]>=i)printf("%d--%d;\n",i,vb[e]); puts("}");}
#define SZ 2333333
ll n;
int m,q,a[SZ];
bool cov[SZ];
int ff[SZ];
int gf(int x) {return (ff[x]==-1)?x:ff[x]=gf(ff[x]);}
void uni(int a,int b)
{int ga=gf(a),gb=gf(b);if(ga^gb)ff[ga]=gb;}
int main()
{
	scanf("%lld%d%d",&n,&m,&q);
	for(int i=1;i<=q;i++)
	scanf("%d",a+i),cov[a[i]]=1;
	#define TJ(r,ans)\
	memset(ff,-1,sizeof(ff));\
	for(int i=0;i<r;i++)\
	{\
		if(cov[i%m])continue;\
		if(i+7<r&&!cov[(i+7)%m]) uni(i,i+7);\
		if(i%7!=6&&i+1<r&&!cov[(i+1)%m]) uni(i,i+1);\
	}\
	for(int i=0;i<r;i++)\
		if(!cov[i%m]) ans+=gf(i)==i;
	int ans1=0; TJ(m*7,ans1)
	int ans2=0; TJ(m*14,ans2)
	ll rd=7*n/m,zg=rd/7,bf=rd%7,ans=0;
	if(zg) ans=ans1+(ans2-ans1)*(zg-1);
	int ans3=0; TJ(m*bf,ans3)
	int ans4=0; TJ(m*bf+m*7,ans4)
	if(zg) ans+=ans4-ans1; else ans+=ans3;
	printf("%lld\n",ans);
}

### Prompt

Please formulate a Cpp solution to the following problem:

Input Format

The input format is following:



n m q
a_1 a_2 ... a_q


Output Format

Print the number of connected part in one line.


Constraints

* n ≤ 10^{12}
* 7n is divisible by m.
* 1 ≤ q ≤ m ≤ 10^5
* 0 ≤ a_1 < a_2 < ... < a_q < m



Scoring

Subtask 1 [100 points]


* n ≤ 100000.

Subtask 2 [90 points]


* m is divisible by 7.
* a_{i + 1} - a_i = 1.

Subtask 3 [200 points]


* m is divisible by 7.

Subtask 4 [110 points]


* There are no additional constraints.



Sample Input 1


7 7 3
1 3 5


Sample Output 1


4


The calendar looks like this:


<image>

Sample Input 2


10 14 8
5 6 7 8 9 10 11 12


Sample Output 2


10


The calendar looks like this:


<image>

Output Format

Print the number of connected part in one line.


Constraints

* n ≤ 10^{12}
* 7n is divisible by m.
* 1 ≤ q ≤ m ≤ 10^5
* 0 ≤ a_1 < a_2 < ... < a_q < m



Scoring

Subtask 1 [100 points]


* n ≤ 100000.

Subtask 2 [90 points]


* m is divisible by 7.
* a_{i + 1} - a_i = 1.

Subtask 3 [200 points]


* m is divisible by 7.

Subtask 4 [110 points]


* There are no additional constraints.

Input Format

The input format is following:



n m q
a_1 a_2 ... a_q

Examples

Input

7 7 3
1 3 5


Output

4


Input

10 14 8
5 6 7 8 9 10 11 12


Output

10

### Response

```cpp
#include <iostream>
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <time.h>
#include <stdlib.h>
#include <string>
#include <bitset>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <algorithm>
#include <sstream>
#include <stack>
#include <iomanip>
using namespace std;
#define pb push_back
#define mp make_pair
typedef pair<int,int> pii;
typedef long long ll;
typedef double ld;
typedef vector<int> vi;
#define fi first
#define se second
#define fe first
#define FO(x) {freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);}
#define Edg int M=0,fst[SZ],vb[SZ],nxt[SZ];void ad_de(int a,int b){++M;nxt[M]=fst[a];fst[a]=M;vb[M]=b;}void adde(int a,int b){ad_de(a,b);ad_de(b,a);}
#define Edgc int M=0,fst[SZ],vb[SZ],nxt[SZ],vc[SZ];void ad_de(int a,int b,int c){++M;nxt[M]=fst[a];fst[a]=M;vb[M]=b;vc[M]=c;}void adde(int a,int b,int c){ad_de(a,b,c);ad_de(b,a,c);}
#define es(x,e) (int e=fst[x];e;e=nxt[e])
#define esb(x,e,b) (int e=fst[x],b=vb[e];e;e=nxt[e],b=vb[e])
#define VIZ {printf("digraph G{\n"); for(int i=1;i<=n;i++) for es(i,e) printf("%d->%d;\n",i,vb[e]); puts("}");}
#define VIZ2 {printf("graph G{\n"); for(int i=1;i<=n;i++) for es(i,e) if(vb[e]>=i)printf("%d--%d;\n",i,vb[e]); puts("}");}
#define SZ 2333333
ll n;
int m,q,a[SZ];
bool cov[SZ];
int ff[SZ];
int gf(int x) {return (ff[x]==-1)?x:ff[x]=gf(ff[x]);}
void uni(int a,int b)
{int ga=gf(a),gb=gf(b);if(ga^gb)ff[ga]=gb;}
int main()
{
	scanf("%lld%d%d",&n,&m,&q);
	for(int i=1;i<=q;i++)
	scanf("%d",a+i),cov[a[i]]=1;
	#define TJ(r,ans)\
	memset(ff,-1,sizeof(ff));\
	for(int i=0;i<r;i++)\
	{\
		if(cov[i%m])continue;\
		if(i+7<r&&!cov[(i+7)%m]) uni(i,i+7);\
		if(i%7!=6&&i+1<r&&!cov[(i+1)%m]) uni(i,i+1);\
	}\
	for(int i=0;i<r;i++)\
		if(!cov[i%m]) ans+=gf(i)==i;
	int ans1=0; TJ(m*7,ans1)
	int ans2=0; TJ(m*14,ans2)
	ll rd=7*n/m,zg=rd/7,bf=rd%7,ans=0;
	if(zg) ans=ans1+(ans2-ans1)*(zg-1);
	int ans3=0; TJ(m*bf,ans3)
	int ans4=0; TJ(m*bf+m*7,ans4)
	if(zg) ans+=ans4-ans1; else ans+=ans3;
	printf("%lld\n",ans);
}

```