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;

typedef pair<int, int> pii;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i,n) rep2(i,0,n)
#define rep2(i,m,n) for(int i=m;i<(n);i++)
#define ALL(c) (c).begin(),(c).end()

int N, M, Q;
int a[100010], b[100010];
bool us[100010];
int pos[100010];
int nums[100010];
bool inc[100010];

int main() {
	cin >> N >> M >> Q;

	rep(i, Q) cin >> a[i];
	int now = 0;
	for (int i = Q-1; i >= 0; --i) {
		if (!us[a[i]]) {
			us[a[i]] = 1;
			b[now++] = a[i];
		}
	}

	for (int i = 1; i <= M; ++i) {
		if (!us[i]) {
			b[now++] = i;
		}
	}

	rep(i, M) {
		pos[b[i]] = i;
	}

	inc[M] = 1; b[M] = 2e5;

	for (int i = M-1; i >= 0; --i) {
		inc[i] = inc[i+1] && (b[i] < b[i+1]);
	}

	nums[0] = N;

	for (int i = Q-1; i >= 0; --i) {
		int p = pos[a[i]];

		if (nums[p] > 0) {
			--nums[p];
			++nums[p+1];
		}
	}

	for (int i = 0; i < M; ++i) {
		if (nums[i] > 0 && !inc[i]) {
			puts("No");
			return 0;
		}
	}
	puts("Yes");
	return 0;
}