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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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

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

outputFormat

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

样例

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

9 2 6