A radio center receivs some signals and needs to classify them according to frequency.

There are standard frequencies known to the center. They have identified different signals which are to be classified. Given the standard signal frequencies freq_standard and frequencies of signals to be classified freq_signal, can you help the radio center identify them?

A signal X belongs to a standard signal Y if the frequency of X is closer to that of Y than to any other frequency. If it is equidistant from two known frequencies, then the signal with higher frequency is chosen.

Consider, for example, freq_standard = [2, 3, 1, 4, 8] and freq_classify = [1, 5, 6]. Frequencies 1 and 5 belong to standard frequencies 1(index=3) and 4(index=4) respectively. Since 6 is equidistant from two standard frequencies, 4 and 8, choose the higher frequency, 8(index=5). The corresponding classifications are [3, 4, 5].

Function Description

Complete the function classifySignals in the editor below. The function must return an integer array denoting the classifications of each frequency.

classifySignals has two parameters -

freq_standard: an integer array

freq_signals: an integer array

Input Format

The first line of input contains 2 space-separated integers: , - the number of strings and the number of queries.

The second line contains space-separated integers, the array freq_standard.

The next line contains space-separated integers, the array freq_signals.

Constraints

  • |freq_standard|
  • |freq_signals|

Output Format

Print lines: each line should contain an integer representing the index of the standard frequency corresponding to the given signal. There is a code stub to handle I/O if you choose to use it.

Sample Input 0

5 5
7 1 12 9 15
2 9 2000 13 4

Sample Output 0

2
4
5
3
1

Explanation 0

The closest frequency to 2 is 1 (index = 2). The closest frequency to 9 is 9 (index = 4). The closest frequency to 2000 is 15 (index = 5). The closest frequency to 13 is 12 (index = 3). The closest frequency to 4 is 7 (index = 1).

Sample Input 1

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

Sample Output 1

1
2
2
2
2
2
2
2
2
2

Explanation 1

The closest frequency to 1 is 1(index = 1). Any frequency which is greater than or equal to 2 will have closest frequency as 2(index = 2).

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