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;

const int N = 100005;

int n, m, q;
int a[N];
vector<int> vec[N];
priority_queue < pair<int, int> > pq;
int last[N];
bool del[N];

// BIT
int T[N];
void upd(int x) { for (; x <= m; x += x & -x) T[x]++; }
int get(int x) { int ret = 0; for (; x > 0; x -= x & -x) ret += T[x]; return ret; }
int get_min() {
	int low = 1, high = m;
	while(low < high) {
		int mid = ((low + high) >> 1);
		if (get(mid) == mid) low = mid + 1;
		else high = mid;
	}
	return low;
}

int main() {
	ios_base::sync_with_stdio(false); cin.tie(0);
	cin >> n >> m >> q;
	for (int i = 1; i <= q; ++i) {
		cin >> a[i];
		pq.push(make_pair(i, a[i]));
		vec[a[i]].push_back(i);
	}
	for (int i = 1; i <= n; ++i) last[i] = q + 1;

	while(!pq.empty()) {
		pair<int, int> top = pq.top(); pq.pop();
		if (del[top.second]) continue;
		int x = top.second;
		del[x] = true;

		int ptr = n;
		while(ptr >= 1 && !vec[x].empty()) {
			int pos = vec[x].back();
			vec[x].pop_back();
			if (last[ptr] > pos) last[ptr] = pos, --ptr;
		}
		// cerr << x << endl;
		// for (int i = 1; i <= n; ++i) cerr << last[i] << ' '; cerr << endl;
		
		if (ptr != 0) { // invalid
			int smallest = get_min();
			if (x != smallest) return cout << "No\n", 0;
			upd(x); // delete x

			while(!pq.empty()) {
				top = pq.top(); pq.pop();
				int nx = top.second;
				if (del[nx]) continue;

				del[nx] = true;
				smallest = get_min();
				if (nx != smallest) return cout << "No\n", 0;
				upd(nx);
			}

			return cout << "Yes\n", 0;
		}

		upd(x); // delete x
	}

	cout << "Yes\n";
}