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>
using namespace std;

const int N = 1e5 + 10;
int n, m, Q, ans = 1, cur, a[N], c[N], p[N], inv[N];

template <class T> inline void in(T &x) {
	x = 0; int f = 1; char ch = getchar();
	for (; ch<'0' || ch>'9';) {if (ch=='-') f=-1; ch = getchar();}
	for (; ch>='0' && ch<='9';) x = x*10 + ch-'0', ch = getchar();
	x *= f;
}

int main() {
	in(n), in(m), in(Q), c[0] = n;
	for (int i = 1; i <= Q; ++i) in(a[i]);
	for (int i = 1; i <= m; ++i) inv[i] = -1;
	for (int i = Q; i; -- i)
		if (inv[a[i]] == -1) {
			inv[a[i]] = ++cur;
			c[cur] = 1, p[cur] = a[i];
		} else if (c[inv[a[i]]] < c[inv[a[i]] - 1]) ++c[inv[a[i]]];
	for (int i = 1; i <= m; ++i) if (inv[i] == -1) p[++cur] = i;
	for (int i = 2; i <= m; ++i)
		if (c[i - 1] != n && p[i - 1] > p[i]) {ans = 0; break;}
	puts(ans ? "Yes" : "No");
	return 0;
}