codeforces 876B

B. Divisiblity of Differences

time limit per test

1 second

memory limit per test

512 megabytes

input

standard input

output

standard output

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, ..., a_n (0 ≤ a_i ≤ 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, ..., b_k — the selected numbers. If there are multiple possible solutions, print any of them.

Examples

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 

比赛前一天还做过类似的题。。。结果当时愣是卡住了。。。气死我了
解题思路：
用数组记录每个数对m取模余数相等的有多少个。。
ac代码：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxn = 1e5+5;
int nu[maxn];
int cnt[maxn];
int main() {
    ios::sync_with_stdio(false);
    int n,k,m,i;
    cin>>n>>k>>m;
    for(i=1;i<=n;++i) {
        cin>>nu[i];
    }
    int ans=-1;
    for(i=1;i<=n;++i) {
        int u=nu[i]%m;
        ++cnt[u];
        if(cnt[u]==k) {
            ans=u;
            break;
        }
    }
    if(ans==-1) cout<<"No"<<endl;
    else {
        cout<<"Yes"<<endl;
        for(int i=1;i<=n;++i) {
            if(nu[i]%m==ans) {
                --k;
                cout<<nu[i]<<" ";
            }
            if(k==0) break;
        }
    }
    return 0;
}