Question

Asha has got a set of integers and he is thinking about what interesting problem statement could be formed from these integers. And Eureka! She found one!

The problem statement goes as follow:

- You have to find the maximum integer among the set of integers and divide the integer by 2.
- Since this is an integer division the result of division will be an integer.
- After division if the integer is greater than 0, then we put the updated integer again in the set of integers.

Asha gives you m queries, each query q[i] means, that q[q[i]ā1] number of operations has already been performed, and its time to perform q[i]th operation. Your task is to tell that for q[i]th operation which integer will get divided.

### Input Format

The first line contains 2 space-separated integers n,m

denoting the number of integers and the number of queries respectively.

The next line contains n space-separated integers followed by m lines.

In the next m lines, the ith line will contain q[i].

### Output format

Output m lines, the ith of which contains the answer for the ith query.

### Constraints

1<=n,m<=10^6

1<=n,m<=10^6

For 1<=i<=m1<=i<=m,

q[i]>q[iā1].

For 0<=i<=n0<=i<=n,

1<=a[i]<=1091<=a[i]<=109

If no integer is present at the time of the query stop the program.

### Example

#### Input

4 6

8 5 3 1

1

2

3

4

6

8

#### Output

8

5

4

3

2

1