You are given a binary string of length n (i. e. a string consisting of n characters '0' and '1').

In one move you can swap two adjacent characters of the string. What is the lexicographically minimum possible string you can obtain from the given one if you can perform no more than k moves? It is possible that you do not perform any moves at all.

Note that you can swap the same pair of adjacent characters with indices i and i+1 arbitrary (possibly, zero) number of times. Each such swap is considered a separate move.

You have to answer q independent test cases.

Input

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

The first line of the test case contains two integers n and k (1 ≤ n ≤ 10^6, 1 ≤ k ≤ 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 (∑ n ≤ 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.

Example

Input


3
8 5
11011010
7 9
1111100
7 11
1111100


Output


01011110
0101111
0011111

Note

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

In the third example, there are enough operations to make the string sorted.
class Case:
    def __init__(self, size, moves, string):
        self.size = size
        self.moves = moves
        self.string = string


SPACE = ' '
ZERO = '0'


def get_case():
    line_elements = input().split(SPACE)
    size = int(line_elements[0])
    moves = int(line_elements[1])
    string = list(input())
    return Case(size, moves, string)


def swap(index, next_zero_index, string):
    string[index], string[next_zero_index] = string[next_zero_index], string[index]
    return string


def solve(case):
    next_zero_index = 0
    remaining_moves = case.moves
    string = case.string
    for index in range(case.size):
        if remaining_moves == 0:
            break

        current_char = string[index]
        if index == 0:
            if current_char == ZERO:
                next_zero_index += 1
            continue

        previous_char = string[index - 1]
        need_to_move = current_char == ZERO and previous_char != ZERO
        if need_to_move:
            desired_moves = index - next_zero_index
            allowed_moves = min(remaining_moves, desired_moves)
            target_index = next_zero_index + abs(desired_moves - allowed_moves)
            string = swap(index, target_index, string)
            remaining_moves -= allowed_moves
            next_zero_index += 1
        elif current_char == ZERO:
            next_zero_index += 1
    return string


if __name__ == "__main__":
    number_of_cases = int(input())
    for i in range(number_of_cases):
        case = get_case()
        solvedList = solve(case)
        solution = "".join(solvedList)
        print(solution)
