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 rep(i,n) for(int i=0;i<n;i++)
using namespace std;

using ll = long long;

int main() {
    ll N, K;
    cin >> N >> K;
    vector<ll> A(N), B(200001, -1), C(N);
    rep(i, N) {
        cin >> A[i];
        if (B[A[i]] == -1) {
            B[A[i]] = i;
        } else {
            C[B[A[i]]] = i;
            B[A[i]] = i;
        }
    }
    rep(i, N) {
        if (B[A[i]] == -1) {
            B[A[i]] = i;
        } else {
            C[B[A[i]]] = i;
            B[A[i]] = i;
        }
    }
    /* /rep(i, N) {
        cout << A[i] << " " << C[i] << endl;
    } */
    ll x = 0, y, d = 1;
    while (true) {
        y = C[x];
        if (y <= x) d++;
        if (y == N - 1) break;
        x = y + 1;
    }
    //cout << d << endl;
    ll l = K % d;
    if (l == 0) {
        cout << "" << endl;
        return 0;
    }
    ll ct = 0;
    x = 0;
    while (ct < l - 1) {
        y = C[x];
        if (y <= x) ct++;
        x = y + 1;
    }
    vector<ll> ans(0);
    while (x < N) {
        y = C[x];
        if (y > x) {
            x = y + 1;
        } else {
            ans.push_back(A[x]);
            x++;
        }
    }
    rep(i, ans.size()) {
        cout << ans[i] << " ";
    }
    cout << endl;
}