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 long long ll;
typedef pair<ll, ll> l_l;
typedef pair<int, int> i_i;
template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
//const ll mod = 1000000007;
int N, M, Q;
int val[100050];
int num[100050];
int inv[100050];
bool canignore[100050];
int a[100050];
int allappeared = 0;

int main() {
    //cout.precision(10);
    cin.tie(0);
    ios::sync_with_stdio(false);
    cin >> N >> M >> Q;
    int index = 0;
    for(int i = Q; i >= 1; i--) cin >> a[i];
    for(int i = 1; i <= Q; i++) {
        if(inv[a[i]] != 0) continue;
        index++;
        inv[a[i]] = index;
        val[index] = a[i];
        if(allappeared == a[i] - 1) canignore[a[i]] = true;
        while(inv[allappeared+1] != 0) allappeared++;
    }
    /*
    while(index >= 1 && allappeared[val[index]]) {
        inv[val[index]] = 0;
        val[index] = 0;
        index--;
    }
    */
    cerr << index << endl;
    for(int i = 1; i <= index; i++) {
        //cerr << val[i] << " " << canignore[val[i]] << endl;
    }
    num[0] = N;
    for(int i = 1; i <= Q; i++) {
        int nowindex = inv[a[i]];
        if(nowindex == 0) continue;
        num[nowindex]++;
        chmin(num[nowindex], num[nowindex-1]);
        /*
        if(num[nowindex] > num[nowindex-1]) {
            cout << "No" << endl;
            return 0;
        }
        */
    }
    for(int i = 1; i <= index; i++) {
        if(!canignore[val[i]] && num[i] != N) {
            cout << "No" << endl;
            return 0;
        }
    }
    cout << "Yes" << endl;
    return 0;
}
