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;
#define For(i,l,r) for (int i = l; i <= r; ++i)
#define Cor(i,l,r) for (int i = l; i >= r; --i)

int n, m, q, A[1111111], bound[1111111], vis[1111111];
vector<int> vec[1111111];
int main() {
	cin >> m >> n >> q;
	For(i,1,q) {
		scanf("%d", &A[i]);
		vec[A[i]].push_back(i);
	}
	For(i,1,m) bound[i] = q + 1;
	int id = 1;
	bool force = false ;
	Cor(i,q,1) {
		if (vis[A[i]]) continue ;
		int idx = vec[A[i]].size() - 1;
		bound[1] = vec[A[i]][idx];
		bool no = false ;		
		For(j,2,m) {
			if (--idx < 0) {
				no = true;
				break ;
			}
			while (bound[j] < vec[A[i]][idx]) {
				if (idx == 0) {
					no = true;
					break ;
				}
				--idx;
			}
			bound[j] = vec[A[i]][idx];
		}
		if (no) {
			force = true;
		}
		vis[A[i]] = true;
		if (force) {
			if (id == A[i]) {
				while (vis[id]) ++id;
				continue ;
			} else {
				puts("No");
				return 0;
			}
		}
		while (vis[id]) ++id;
	}
	puts("Yes");
	return 0;
}