Binary String Minimizing

Description:

Input:

The first line of the input contains one integer $$$q$$$ ($$$1 \le q \le 10^4$$$) — the number of test cases.

The first line of the test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^6, 1 \le k \le n^2$$$) — the length of the string and the number of moves you can perform.

The second line of the test case contains one string consisting of $$$n$$$ characters '0' and '1'.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$ ($$$\sum n \le 10^6$$$).

Output:

For each test case, print the answer on it: the lexicographically minimum possible string of length $$$n$$$ you can obtain from the given one if you can perform no more than $$$k$$$ moves.

Sample Input:

3
8 5
11011010
7 9
1111100
7 11
1111100

Sample Output:

01011110
0101111
0011111

Note:

In the first example, you can change the string as follows: $$$1\underline{10}11010 \rightarrow \underline{10}111010 \rightarrow 0111\underline{10}10 \rightarrow 011\underline{10}110 \rightarrow 01\underline{10}1110 \rightarrow 01011110$$$.

In the third example, there are enough operations to make the string sorted.