We have a sequence of N \times K integers: X=(X_0,X_1,\cdots,X_{N \times K-1}). Its elements are represented by another sequence of N integers: A=(A_0,A_1,\cdots,A_{N-1}). For each pair i, j (0 \leq i \leq K-1,\ 0 \leq j \leq N-1), X_{i \times N + j}=A_j holds.

Snuke has an integer sequence s, which is initially empty. For each i=0,1,2,\cdots,N \times K-1, in this order, he will perform the following operation:

* If s does not contain X_i: add X_i to the end of s.
* If s does contain X_i: repeatedly delete the element at the end of s until s no longer contains X_i. Note that, in this case, we do not add X_i to the end of s.



Find the elements of s after Snuke finished the operations.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq K \leq 10^{12}
* 1 \leq A_i \leq 2 \times 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
A_0 A_1 \cdots A_{N-1}


Output

Print the elements of s after Snuke finished the operations, in order from beginning to end, with spaces in between.

Examples

Input

3 2
1 2 3


Output

2 3


Input

5 10
1 2 3 2 3


Output

3


Input

6 1000000000000
1 1 2 2 3 3


Output




Input

11 97
3 1 4 1 5 9 2 6 5 3 5


Output

9 2 6
#include<bits/stdc++.h>
#include <array>
using namespace std;
using ULL = unsigned long long;
using UL = unsigned;
using LL = long long;
#define rep(i, n) for(UL i = 0; i < (n); i++)

struct Problem {

	void Solve() {
		UL N; cin >> N;
		ULL K; cin >> K;
		ULL NK = N * K;
		vector<UL> S(N); rep(i, N) { cin >> S[i]; S[i]--; }
		vector<UL> Nx(N);
		{
			vector<UL> P; P.assign(200000, (UL)-1);
			rep(i, N) {
				if (P[S[i]] != (UL)-1) Nx[P[S[i]]] = i + 1;
				P[S[i]] = i;
			}
			rep(i, N) {
				if (P[S[i]] != (UL)-1) if (P[S[i]] < N) Nx[P[S[i]]] = N + i + 1;
				P[S[i]] = i + N;
			}
		}
		ULL p = 0;
		do { p += (Nx[p % N] - p % N); } while (p % N);
		ULL q = NK - NK % p;
		vector<UL> ans;
		while (q < NK) {
			ULL nxq = q + (Nx[q % N] - q % N);
			if(nxq <= NK) q += (Nx[q % N] - q % N);
			else {
				ans.push_back(S[q % N] + 1); q++;
			}
		}
		rep(i, ans.size()) {
			if (i != 0) cout << " ";
			cout << ans[i];
		}cout << endl;
	}

	Problem();
};
int main() {
	unique_ptr<Problem> p(new Problem());
	p->Solve();
	return 0;
}
Problem::Problem() {
	cout << fixed << setprecision(10);
}
