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>
using namespace std;
const int maxn = 2e5 + 7;
long long n, k, d;
int a[maxn], lst[maxn], to[maxn], zz[maxn], t, hs[maxn];

int main() {
	scanf("%lld%lld", &n, &k);
	for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
	for (int i = n; i; --i) lst[a[i]] = i;
	for (int i = n; i; --i) {
		to[i] = lst[a[i]];
		lst[a[i]] = i;
	}
	int pos = 1;
	do {
		if(to[pos] <= pos) ++d;
		if(to[pos] == n) ++d;
		pos = to[pos] % n + 1;
	}while(pos != 1);
	k %= d;
	if(k == 0) return 0;
	pos = 1;
	while(1) {
		if(to[pos] <= pos) {
			if(k > 1) --k;
			else break;
		}
		pos = to[pos] % n + 1;
	}
	for (int i = pos; i <= n; ++i) {
		if(hs[a[i]]) {
			//cerr << a[i] << endl;
			while(zz[t] != a[i]) 
				hs[zz[t--]] = 0;
			hs[zz[t--]] = 0;
		}
		else {
			hs[a[i]] = 1;
			zz[++t] = a[i];
		}
	}
	for (int i = 1; i <= t; ++i) printf("%d ", zz[i]);
	printf("\n");
	return 0;
}