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>

#define itn int
#define all(x) (x).begin(), (x).end()
#define make_unique(x) sort(all((x))); (x).resize(unique(all((x))) - (x).begin())

#define random_shuffle(...) shuffle(__VA_ARGS__, rng)
#define rand() rng()

using namespace std;

inline int nxt() {
	int x;
	scanf("%d", &x);
	return x;
}

int main() {
	mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

	int n = nxt();
	long long k;
	scanf("%lld", &k);
	vector<int> a(n * 2);
	for (int i = 0; i < n; ++i) {
		a[i] = a[i + n] = nxt();
	}

	vector<int> nx(2 * n, -1);
	map<int, int> M;
	for (int i = 2 * n - 1; i >= 0; --i) {
		if (M.count(a[i])) {
			nx[i] = M[a[i]];
		}
		M[a[i]] = i;
	}

	long long total = 0;
	int idx = 0;
	do {
		total += nx[idx] - idx + 1;
		idx = (nx[idx] + 1) % n;
	} while (idx > 0);
	assert(total % n == 0);
	k %= total / n;
	k *= n;
	while (nx[idx] - idx + 1 < k) {
		k -= nx[idx] - idx + 1;
		idx = (nx[idx] + 1) % n;
	}

	vector<int> b;
	set<int> S;
	while (k--) {
		if (S.count(a[idx])) {
			while (S.count(a[idx])) {
				S.erase(b.back());
				b.pop_back();
			}
		} else {
			S.insert(a[idx]);
			b.push_back(a[idx]);
		}
		idx = (idx + 1) % n;
	}

	for (int x : b) {
		printf("%d ", x);
	}
	printf("\n");

	return 0;
}