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>
// iostream is too mainstream
#include <cstdio>
// bitch please
#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <list>
#include <cmath>
#include <iomanip>
#include <time.h>
#define dibs reserve
#define OVER9000 1234567890123456789LL
#define ALL_THE(CAKE,LIE) for(auto LIE =CAKE.begin(); LIE != CAKE.end(); LIE++)
#define tisic 47
#define soclose 1e-8
#define chocolate win
// so much chocolate
#define patkan 9
#define ff first
#define ss second
#define abs(x) ((x < 0)?-(x):x)
#define uint unsigned int
#define dbl long double
#define pi 3.14159265358979323846
using namespace std;
// mylittledoge

typedef long long cat;

#ifdef DONLINE_JUDGE
	// palindromic tree is better than splay tree!
	#define lld I64d
#endif

int main() {
	cin.sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(10);
	int N,M,Q;
	cin >> N >> M >> Q;
	vector<int> A(Q),seq;
	for(int i =0; i < Q; i++) {
		cin >> A[i];
		A[i]--;
	}
	vector<bool> vis(M,0);
	for(int i =Q-1; i >= 0; i--) if(!vis[A[i]]) {
		seq.push_back(A[i]);
		vis[A[i]] =1;
	}
	for(int i =0; i < M; i++) if(!vis[i]) {
		seq.push_back(i);
		vis[i] =1;
	}
	vector<int> rev(M);
	for(int i =0; i < M; i++) rev[seq[i]] =i;

	vector<int> cnt(M+1,0);
	cnt[0] =N;
	for(int i =0; i < M; i++) vis[i] =0;
	for(int i =Q-1; i >= 0; i--) {
		int id =rev[A[i]];
		if(cnt[id] == 0 && !vis[A[i]]) {
			cout << "No\n";
			return 0;
		}
		if(cnt[id] == 0) continue;
		vis[A[i]] =1;
		cnt[id]--;
		cnt[id+1]++;
	}

	int mid =M-1;
	while(mid > 0 && seq[mid-1] < seq[mid]) mid--;
	for(int i =0; i < mid; i++) if(cnt[i]) {
		cout << "No\n";
		return 0;
	}
	cout << "Yes\n";
	return 0;}

// look at my code
// my code is amazing
