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;
int N, M, Q;
const int _ = 100096;
int a[_], r[_], id[_], s[_];
bool vis[_];

int main() {
	scanf("%d%d%d", &N, &M, &Q);
	int t = 1;	
	for(int i = 1; i <= Q; ++i) {
		scanf("%d", a + i);
		if(a[i] >= t-1) t = a[i];
	}
	if(t == 1) return puts("Yes"), 0;
	int c = 0;
	for(int i = Q; i >= 1; --i)
		if(!vis[a[i]]) {
			r[++c] = a[i];
			vis[a[i]]= true;
		}
	for(int i =1; i <= M; ++i)
		if(!vis[i]) r[++c] = i;
	for(int i = 1; i <= M; ++i)
		id[r[i]] = i;
	int init = M;
	for(;init > 1 && r[init] > r[init - 1]; -- init);
	int worst = init;
	s[init] = N;
	for(int i = 1; i <= Q; ++i) {
		int k = id[a[i]];
		if(s[k + 1]) {
			s[k + 1]--;
			++s[k];
			if(k + 1 == worst && !s[k + 1])
				--worst;
		} else {
			if(k > worst) {
				--s[worst];
				++s[worst = k];
			} 
		}
	}
	puts(worst > 1? "No": "Yes");
}
