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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
typedef pair<int,P> P1;
typedef pair<P,P> P2;
#define pu push
#define pb push_back
#define mp make_pair
#define eps 1e-7
#define INF 1000000000
#define mod 1000000007
#define fi first
#define sc second
#define rep(i,x) for(int i=0;i<x;i++)
#define repn(i,x) for(int i=1;i<=x;i++)
#define SORT(x) sort(x.begin(),x.end())
#define ERASE(x) x.erase(unique(x.begin(),x.end()),x.end())
#define POSL(x,v) (lower_bound(x.begin(),x.end(),v)-x.begin())
#define POSU(x,v) (upper_bound(x.begin(),x.end(),v)-x.begin())
int n,m,q,a[100005],d;
multiset<int>M;
map<int,int>S;
vector<int>vi;
int main(){
	cin>>n>>m>>q; rep(i,q)cin>>a[q-1-i]; rep(i,n) M.insert(0);
	rep(i,q){
		if(S.find(a[i]) == S.end()){
			S[a[i]] = ++d; vi.pb(a[i]);
		}
		int D = S[a[i]];
		multiset<int>::iterator it=M.lower_bound(D-1); int v = *it;
		M.erase(it);
		M.insert(max(v,D));
	}
	for(int i=1;i<=m;i++) if(S.find(i) == S.end()) vi.pb(i);
	int lim=0;
	for(int i=vi.size()-2;i>=0;i--){
		if(vi[i] > vi[i+1]){
			lim=i+1; break;
		}
	}
	for(multiset<int>::iterator it=M.begin();it!=M.end();++it){
		if((*it) < lim){
			puts("No"); return 0;
		}
	}
	puts("Yes");
}