There are N arrays. The length of each array is M and initially each array contains integers (1，2，...，M) in this order.

Mr. Takahashi has decided to perform Q operations on those N arrays. For the i-th (1≤i≤Q) time, he performs the following operation.

* Choose an arbitrary array from the N arrays and move the integer a_i (1≤a_i≤M) to the front of that array. For example, after performing the operation on a_i=2 and the array (5，4，3，2，1), this array becomes (2，5，4，3，1).



Mr. Takahashi wants to make N arrays exactly the same after performing the Q operations. Determine if it is possible or not.

Constraints

* 2≤N≤10^5
* 2≤M≤10^5
* 1≤Q≤10^5
* 1≤a_i≤M

Input

The input is given from Standard Input in the following format:


N M
Q
a_1 a_2 ... a_Q


Output

Print `Yes` if it is possible to make N arrays exactly the same after performing the Q operations. Otherwise, print `No`.

Examples

Input

2 2
3
2 1 2


Output

Yes


Input

3 2
3
2 1 2


Output

No


Input

2 3
3
3 2 1


Output

Yes


Input

3 3
6
1 2 2 3 3 3


Output

No
#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<map>
#include<queue>
#include<vector>
#include<cstdlib>
#define range(i,a,b) for(int i = (a); i <= (b); i++)
#define rep(i,b) for(int i = 1; i <= (b); i++)
#define rrep(i,b) for(int i = (b); i >= 1; i--)
#define all(a) (a).begin(), (a).end()
#define show(x) cout << #x << " = " << (x) << endl;
using namespace std;
typedef long long ll;
const int N=1e5+11,INF=~0u>>2;
bool vis[N],flag=1;
int n,m,q,a[N],b[N],id[N],cnt[N],len;
int read(){
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-') f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return f*x;
}
int main(){
//	freopen("ex.in","r",stdin);
	n=read();m=read();q=read();
	rep(i,q) a[i]=read();
	rrep(i,q) if(!vis[a[i]]) b[++len]=a[i],vis[a[i]]=1;
	rep(i,m) if(!vis[i]) b[++len]=i;
//	rep(i,m) show(b[i]);
//	show(len);
	rep(i,m) id[b[i]]=i;
	cnt[0]=n;
	rep(i,m) vis[i]=0;
	rrep(i,q){
		int t=id[a[i]];
		if(cnt[t-1]>0) cnt[t-1]--,cnt[t]++,vis[t]=1;
		else if(!vis[t]){
			flag=0;
			break;
		}
	}
	len=0;
	while(cnt[len]==0) len++;
	range(i,len+1,m-1) flag&=b[i]<b[i+1];
	puts(flag?"Yes":"No");
	return 0;
}