Pivots

B: Pivots

problem

Given a permutation of length N, a_1, a_2, ..., a_N, which is a permutation of integers from 1 to N. Also, Q queries are given in order for this permutation. In the i-th query, you have to do the following:

• The value q_i (1 \ leq q_i \ leq N) is given. In the permutation \ {a_1, a_2, ..., a_N \}, where L is the permutation on the left side of q_i and R is the permutation on the right side of q_i, the original permutation L \ q_i \ R is R \ Change to q_i \ L. That is, when q_ {i} = a_j, the permutations \ {a_1, ..., a_ {j-1}, a_j, a_ {j + 1}, ..., a_N \} are \ { Change to a_ {j + 1}, ..., a_N, a_j, a_1, ..., a_ {j-1} \}.

The permutations L and R may be empty. For example, if L is empty, change q_i \ R to R \ q_i. The same is true when R is empty.

Output the permutation after processing these Q queries in order for the given permutation on one line.

Input format

N Q a_1 a_2 ... a_N q_1 q_2 ... q_Q

All inputs are integers.

The first row gives the number of elements in the permutation N and the number of queries Q, separated by blanks. In the second line, permutations a_1, a_2, ..., a_N, in which integers from 1 to N are rearranged, are given separated by blanks. The third line gives Q queries, separated by blanks. q_i represents the i-th query.

Constraint

• 1 \ leq N \ leq 10 ^ 5
• 1 \ leq Q \ leq 10 ^ 5
• 1 \ leq a_i \ leq N
• a_i is different
• 1 \ leq q_i \ leq N

Output format

Output the permutation after processing all the queries in order on one line.

Input example 1

5 2 1 5 3 2 4 5 2

Output example 1

4 5 1 2 3

• The first query changes the permutation to \ {3, 2, 4, 5, 1 \}.
• The second query changes the permutation to \ {4, 5, 1, 2, 3 \}.

Input example 2

5 1 1 2 3 4 5 Five

Output example 2

5 1 2 3 4

Example

Input

5 2 1 5 3 2 4 5 2

Output

4 5 1 2 3

inputFormat

outputFormat

Output the permutation after processing these Q queries in order for the given permutation on one line.

Input format

N Q a_1 a_2 ... a_N q_1 q_2 ... q_Q

All inputs are integers.

The first row gives the number of elements in the permutation N and the number of queries Q, separated by blanks. In the second line, permutations a_1, a_2, ..., a_N, in which integers from 1 to N are rearranged, are given separated by blanks. The third line gives Q queries, separated by blanks. q_i represents the i-th query.

Constraint

• 1 \ leq N \ leq 10 ^ 5
• 1 \ leq Q \ leq 10 ^ 5
• 1 \ leq a_i \ leq N
• a_i is different
• 1 \ leq q_i \ leq N

Output format

Output the permutation after processing all the queries in order on one line.

Input example 1

5 2 1 5 3 2 4 5 2

Output example 1

4 5 1 2 3

• The first query changes the permutation to \ {3, 2, 4, 5, 1 \}.
• The second query changes the permutation to \ {4, 5, 1, 2, 3 \}.

Input example 2

5 1 1 2 3 4 5 Five

Output example 2

5 1 2 3 4

Example

Input

5 2 1 5 3 2 4 5 2

Output

4 5 1 2 3

样例

5 2
1 5 3 2 4
5 2

4 5 1 2 3