Syrjälä's prison has $n$ inmates numbered $1,2,\dots,n$. Each of the inmates has their own cell and each of the cells has a unique key. The guards have invented a neat convenience feature: the keys to the cells are stored in an array of tiny lockers. The lockers can be opened with a master key or with one of the other cell keys in case the master key gets lost. This is obviously terrible for security. The $i$-th locker can be opened with the key to cell $k_i$. No two lockers can be opened with the same cell key. You will be given $q$ queries numbered $1,2,\dots,q$. The $i$-th query asks the number of inmates that can escape if they get a hold of the key to cell $x_i$.

Input

The first line contains two integers $n$ and $q$. The second line contains $n$ integers $k_1,\,k_2,\dots\,k_n$, and the third line contains $q$ integers $x_1,\,x_2,\,\dots,\,x_q$

Output

Print the answers to the queries on a single line.

Constraints

• $1 \leq n, q \leq 10^5$
• $1 \leq k_i \leq n$
• $1 \leq x_i \leq n$
• $k_i \neq k_j$ if $i \neq j$

Example 1

Input:

5 5
1 3 2 4 5 
3 5 3 4 4

Output:

2 1 2 1 1

Example 2

Input:

10 6
8 6 3 10 1 5 7 2 4 9 
9 3 5 1 7 5

Output:

3 1 5 5 1 5

Example 3

Input:

1 1
1
1

Output:

1