<image>

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:

  * If the element is dead and it has exactly 1 alive neighbor in the current state of the array, then on the next iteration it will become alive. For an element at index i the neighbors would be elements with indices i - 1 and i + 1. If there is no element at that index, it is considered to be a dead neighbor. 
  * William is a humane person so all alive elements stay alive. 



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.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^3). Description of the test cases follows.

The first line of each test case contains two integers n and m (2 ≤ n ≤ 10^3, 1 ≤ m ≤ 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.

Output

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.

Example

Input


4
11 3
01000000001
10 2
0110100101
5 2
10101
3 100
000


Output


11111001111
1110111101
10101
000

Note

Sequence of iterations of evolution for the first test case 

  * 01000000001 — initial state 
  * 11100000011 — first iteration of evolution 
  * 11110000111 — second iteration of evolution 
  * 11111001111 — third iteration of evolution 



Sequence of iterations of evolution for the second test case 

  * 0110100101 — initial state 
  * 1110111101 — first iteration of evolution 
  * 1110111101 — second iteration of evolution 
#include <bits/stdc++.h>
using namespace std;
using namespace std::chrono;

/*-------------------------------------*---------------------------------------*/

typedef long long ll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef pair<ll, ll> pll;
typedef vector<pll> vpll;
typedef tuple<ll, ll, ll> tlll;

#define F(i, m, n) for (ll i = m; i < n; i++)
#define Fr(j, n, m) for (ll j = n; j >= m; j--)
#define ff first
#define ss second
#define min min<ll>
#define max max<ll>
#define all(c) c.begin(), c.end()
/*-------------------------------------*---------------------------------------*/

#define godspeed                                                               \
  ios_base::sync_with_stdio(false);                                            \
  cin.tie(NULL);                                                               \
  cout.tie(NULL)
#define deb(x) cout << #x << "=" << x << endl
#define cout_array(a)                                                          \
  cout << #a << "=";                                                           \
  for (auto x : a) {                                                           \
    cout << x << " ";                                                          \
  }                                                                            \
  cout << endl

/*-------------------------------------*---------------------------------------*/
/**
 * Calcultes greatest Common divison using Euclid's division Lemma
 * Use __gcd(a,b) : inbuilt function
 */

/**
 * Calculates (x^y)%z Using Binary Exponentiation . Similar to pow(x,y,z)
 * function of python
 *
 * @param   x,y Input numbers
 * @param   z if not specified default to 1e18
 * @returns pow(x,y) modulo z
 */

const ll MAX_PRIME = 1e9 + 7;
const ll INF = 1e18 + 1;
const pll EXTREMA = make_pair(INF, -INF);
ll fast_pow(ll x, ll y, ll z = INF) {
  if (y == 0)
    return 1 % z;
  else if (y == 1)
    return x % z;
  if (y % 2 == 0) {
    ll res = fast_pow(x, y / 2, z);
    return (res * res) % z;
  } else {
    ll res = fast_pow(x, y / 2, z);
    ll temp = (res * res) % z;
    return ((x % z) * temp) % z;
  }
}

/*-------------------------------------*---------------------------------------*/

/**
 * DFS
 * vis.clear();vis.assign(n,0);
 * adj.clear();adj.resize(n);
 */
const ll N = 1e5 + 1;
vll vis(N);
vvll adj(N);
void dfs(ll u) {
  if (vis[u])
    return;

  vis[u] = 1;

  for (ll v : adj[u]) {
    if (vis[v])
      continue;
    // do something
    dfs(v);
  }
  return;
}
/*-------------------------------------*---------------------------------------*/

/**
 * @author Abhay Mishra
 * @date   May 24 2021
 */
/*-------------------------------------*---------------------------------------*/

int main() {

#ifndef ONLINE_JUDGE
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
  auto start = high_resolution_clock::now();
#endif
  godspeed;
  ll t;
  cin >> t;
  while (t--) {
    ll n,m;
    cin >> n>>m;
    string s;
    cin>>s;
    string b(n,'0');
    ll k = 0;
    vll a;
    F(i,0,n){
      if(s[i]=='1'){
        a.push_back(i);
        k = m;
        b[i] = '1';
      }
      else if(k>0){
        b[i] = '1';
        k--;
      }
    }
    k = 0;
    Fr(i,n-1,0){
      if(s[i]=='1'){
        k = m;
        b[i] = '1';
      }
      else if(k>0){
        b[i] = '1';
        k--;
      }
    }
    ll temp;
    F(i,1,a.size()){
      temp = (a[i] + a[i-1])/2;
      if(temp*2 != a[i]+a[i-1])continue;
      b[temp] = '0';
    }
    cout<<b<<endl;
  }
#ifndef ONLINE_JUDGE
  auto stop = high_resolution_clock::now();
  auto duration = duration_cast<milliseconds>(stop - start);
  cout << "Total Time taken to execute the program is :" << duration.count()
       << " ms" << endl;
#endif
  return 0;
}