CF 1811A - Insert Digit

You have a positive number of length n

 and one additional digit.

You can insert this digit anywhere in the number, including at the beginning or at the end.

Your task is to make the result as large as possible.

For example, you have the number 76543

, and the additional digit is 4

. Then the maximum number you can get is 765443

, and it can be obtained in two ways — by inserting a digit after the 3

th or after the 4

th digit of the number.

Input

The first line contains a single integer t

 (1≤t≤104) — the number of test cases.

The descriptions of the test cases follow.

The first line of the description of each test case contains two integers n

 and d (1≤n≤2⋅105; 0≤d≤9) — the length of the number and an additional digit, respectively.

The second line of the description of each test case contains a string consisting of n

 digits — the number that you have initially. It is guaranteed that the number does not contain leading zeros.

It is guaranteed that the sum of n

 for all test cases does not exceed 2⋅105

.Output

For each test case, output a string consisting of n+1digits — the maximum possible number that can be obtained.

Example

input

11

5 4

76543

1 0

1

2 5

44

3 6

666

5 6

13579

5 8

97531

19 4

9876543210123456789

5 7

73737

8 1

20000000

7 0

7058959

12 1

828127127732

output

765443

10

544

6666

613579

987531

98765443210123456789

773737

210000000

70589590

8281271277321

找到第一个比给定字符小的数，将这个数插入到此数之前即可当然如果都找不到那就放在最后面。

下面是代码；