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>
 
const int MAXN = 1E5 + 10;
 
int n, m, Q;
int a[MAXN];
int b[MAXN], id[MAXN];
bool vis[MAXN];
int cnt[MAXN];
 
int main(){
	scanf("%d%d", &n, &m);
	scanf("%d", &Q);
	for (int i = 1; i <= Q; ++i)
		scanf("%d", &a[i]);
	for (int k = 0, j = Q; j > 0; --j)
		if (!vis[a[j]])
			b[++k] = a[j], vis[a[j]] = true;
	for (int j = m, i = m; i > 0; --i)
		if (!vis[i])
			b[j--] = i;
	for (int i = 1; i <= m; ++i)
		id[b[i]] = i;
 
	bool flag = true;
	cnt[0] = n;
	for(int i=1;i<=m;++i) vis[i]=0;
	for (int i = Q; i > 0; --i){
		int t = id[a[i]];
		if (cnt[t - 1] > 0){
			--cnt[t - 1];
			++cnt[t];
			vis[t] = true;
		}
		else if (!vis[t]){
			flag = false;
			break;
		}
	}
 
	int l;
	for (l = 0; cnt[l] == 0; ++l);
	for (int i = l + 1; i < m; ++i)
		flag &= b[i] < b[i + 1];
	puts(flag ? "Yes" : "No");
	return 0;
}