William really likes the cellular automaton called "Game of Life" so he decided to make his own version. For simplicity, William decided to define his cellular automaton on an array containing $$$n$$$ cells, with each cell either being alive or dead.
Evolution of the array in William's cellular automaton occurs iteratively in the following way:
Check the note section for examples of the evolution.
You are given some initial state of all elements and you need to help William find the state of the array after $$$m$$$ iterations of evolution.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$). Description of the test cases follows.
The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 10^3, 1 \le m \le 10^9$$$), which are the total number of cells in the array and the number of iterations.
The second line of each test case contains a string of length $$$n$$$ made up of characters "0" and "1" and defines the initial state of the array. "1" means a cell is alive and "0" means it is dead.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^4$$$.
In each test case output a string of length $$$n$$$, made up of characters "0" and "1" — the state of the array after $$$m$$$ iterations of evolution.
4 11 3 01000000001 10 2 0110100101 5 2 10101 3 100 000
11111001111 1110111101 10101 000
Sequence of iterations of evolution for the first test case
Sequence of iterations of evolution for the second test case