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
/* ***************************************
Author        :Scau.ion
Created Time  :2016/09/24 20:56:18 UTC+8
File Name     :ion.cpp
*************************************** */

#include <bits/stdc++.h>

#define LL long long
#define ULL unsigned long long
#define PB push_back
#define MP make_pair
#define PII pair<int,int>
#define VI vector<int>
#define VPII vector<PII>
#define X first
#define Y second
#define IOS ios::sync_with_stdio(0);cin.tie(0);
#define IN freopen("in", "r", stdin);
#define OUT freopen("out", "w", stdout);

using namespace std;

const int maxn=100010;

int seat[maxn],a[maxn],sum[maxn],num[maxn];
bool finish[maxn];

int main()
{
	int n,m,q;
    scanf("%d%d%d",&n,&m,&q);
    for (int j=1;j<=q;++j)
    {
        scanf("%d",&a[j]);
    }
    bool flag=1;
    int last=0;
    for (int j=q;j>0;--j)
    {
        if (a[j]>last)
        {
            if (a[j]==last+1) ++last;
            else
            {
                flag=0;
                break;
            }
        }
    }
    if (flag)
    {
        printf("Yes\n");
        return 0;
    }
    int cnt=0;
    for (int j=q;j>0;--j)
    {
        int tis=a[j];
        if (seat[tis]==0)
        {
            ++cnt;
            seat[tis]=cnt;
            sum[cnt]=1;
            num[cnt]=tis;
        }
        else
        {
            if (finish[tis]) continue;
            int st=seat[tis];
            ++sum[st];
            if (st>1&&sum[st]>sum[st-1]) --sum[st];
            if (sum[st]==n)
            {
                finish[tis]=1;
                continue;
            }
        }
    }
    if (flag)
    {
        printf("No\n");
        return 0;
    }
    int nx=1;
    while (nx<=m&&finish[nx]) ++nx;
    for (int j=1;j<=cnt;++j)
    {
        if (sum[j]<n)
        {
            if (num[j]!=nx)
            {
                flag=1;
                break;
            }
            else
            {
                ++nx;
                while (nx<=m&&finish[nx]) ++nx;
            }
        }
    }
    if (flag) printf("No\n");
    else printf("Yes\n");
	return 0;
}
