#include "bits/stdc++.h"
using namespace std;

using i64 = long long;

#ifdef LOCAL
#include "debug.h"
#else
#define debug(...) 42
#endif

bool check(int n, int k, vector<int> a, int target_max_worry) {
  vector<int> current_worries = a;
  for (int op = 0; op < k; ++op) {
    int max_worry = *max_element(current_worries.begin(), current_worries.end());
    if (max_worry <= target_max_worry) {
      return true;
    }
    int best_confider = -1;
    int min_next_max_worry = max_worry + 1;
    for (int p = 0; p < n - 1; ++p) {
      vector<int> next_worries = current_worries;
      next_worries[p + 1] += next_worries[p] / 2;
      next_worries[p] /= 2;
      int next_max_worry = *max_element(next_worries.begin(), next_worries.end());
      if (next_max_worry < min_next_max_worry) {
        min_next_max_worry = next_max_worry;
        best_confider = p;
      }
    }
    if (best_confider == -1) {
      break;
    }
    current_worries[best_confider + 1] += current_worries[best_confider] / 2;
    current_worries[best_confider] /= 2;
  }
  return *max_element(current_worries.begin(), current_worries.end()) <= target_max_worry;
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  int t;
  cin >> t;
  while (t--) {
    int n, k;
    cin >> n >> k;
    vector<int> a(n);
    for (int i = 0; i < n; ++i) {
      cin >> a[i];
    }

    int low = 0, high = *max_element(a.begin(), a.end());
    int min_max_worry = high;
    while (low <= high) {
      int mid = low + (high - low) / 2;
      if (check(n, k, a, mid)) {
        min_max_worry = mid;
        high = mid - 1;
      } else {
        low = mid + 1;
      }
    }

    i64 s = (i64)min_max_worry;
    for (int i = 0; i < k; ++i) {
      s *= 2;
    }

    if (s == 0) {
      cout << 0 << '\n';
    } else {
      string binary_s = "";
      while (s > 0) {
        binary_s = (s % 2 == 0 ? "0" : "1") + binary_s;
        s /= 2;
      }
      cout << binary_s << '\n';
    }
  }
  return 0;
}