You are given a multiset of n integers. You should select exactly k of them in a such way that the difference between any two of them is divisible by m, or tell that it is impossible.

Numbers can be repeated in the original multiset and in the multiset of selected numbers, but number of occurrences of any number in multiset of selected numbers should not exceed the number of its occurrences in the original multiset.

Input

First line contains three integers n, k and m (2 ≤ k ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — number of integers in the multiset, number of integers you should select and the required divisor of any pair of selected integers.

Second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 109) — the numbers in the multiset.

Output

If it is not possible to select k numbers in the desired way, output «No» (without the quotes).

Otherwise, in the first line of output print «Yes» (without the quotes). In the second line print k integers b1, b2, ..., bk — the selected numbers. If there are multiple possible solutions, print any of them.

Example

Input

3 2 3

1 8 4

Output

Yes

1 4

Input

3 3 3

1 8 4

Output

No

Input

4 3 5

2 7 7 7

Output

Yes

2 7 7

题意：

给出n个数字，问能否从中挑选出k个数，使这k个数任意之间的差能被m整除。

题解：

k个数对m取模的结果肯定都是相等的，记录一下取模后结果相等的有多少个数就OK。

#include
    
     #include
     
      #include
      
       using namespace std;const int maxn=1e5+5;int a[maxn];int has[maxn];int main(){    int n,k,m;    while(cin>>n>>k>>m)    {        memset(has,0,sizeof(has));        int flag=-1;        for(int i=0;i
       
        >a[i];            if(++has[a[i]%m]>=k)            {                flag=a[i]%m;            }        }        if(flag==-1)            cout<<"No"<