You have a sequence a1,a2,…,ana1,a2,…,an of length nn, consisting of integers between 11 and mm. You also have a string ss, consisting of mm characters B.
You are going to perform the following nn operations.
Find the lexicographically smallest string you can get after these operations.
A string xx is lexicographically smaller than a string yy of the same length if and only if in the first position where xx and yy differ, the string xx has a letter that appears earlier in the alphabet than the corresponding letter in yy.
The first line contains the number of test cases tt (1≤t≤20001≤t≤2000).
The first line of each test case contains two integers nn and mm (1≤n,m≤501≤n,m≤50) — the length of the sequence aa and the length of the string ss respectively.
The second line contains nn integers a1,a2,…,ana1,a2,…,an (1≤ai≤m1≤ai≤m) — the sequence aa.
For each test case, print a string of length mm — the lexicographically smallest string you can get. Each character of the string should be either capital English letter A or capital English letter B.
6
4 5
1 1 3 1
1 5
2
4 1
1 1 1 1
2 4
1 3
2 7
7 5
4 5
5 5 3 5
ABABA
BABBB
A
AABB
ABABBBB
ABABA