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<stdio.h>
#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define f(i,x,n) for (int i = x;i < n;++i)

vector<int> v[100000], V;
int l[100001], x[100000];

void NO() {
	printf("No\n");
	exit(0);
}

int main() {
	int n, m, q;
	scanf("%d%d%d", &n, &m, &q);
	f(i, 0, q)scanf("%d", x + i);
	for (int i = q - 1; i >= 0; --i) {
		int &d = l[x[i]];
		if (d == n)continue;
		if (!d)V.push_back(x[i]);
		if (V[v[d].size()] != x[i])continue;
		v[d].push_back(x[i]);
		++d;
	}
	int i = V.size();
	int j = 1;
	while (l[j])++j;
	for (--j; j && i; --j)if (V[i - 1] == j)--i;
	f(j, 0, n)f(k, 0, V.size()) {
		if (k >= v[j].size()) {
			if (k < i)NO();
			break;
		}
		if (v[j][k] != V[k])NO();
	}
	printf("Yes\n");
}