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

using i64 = long long;

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

int main() {
    cin.tie(0)->sync_with_stdio(0);
    int T;
    cin >> T;
    while (T--) {
        int n, k;
        cin >> n >> k;
        vector<double> a(n);
        for (int i = 0; i < n; i++) {
            int x;
            cin >> x;
            a[i] = x;
        }
        k = min(k, n - 1);
        double left = 0, right = *max_element(a.begin(), a.end());
        vector<int> x(n), x_min(n);
        for (int iter = 0; iter < 100; iter++) {
            double mid = (left + right) / 2;
            bool ok = true;
            for (int i = 0; i < n; i++) {
                if (mid >= a[i]) {
                    x_min[i] = 0;
                } else {
                    double ratio = a[i] / mid;
                    x_min[i] = ceil(log2(ratio));
                }
            }
            x.back() = 0;
            for (int i = n - 2; i >= 0; i--) {
                x[i] = min(x[i + 1], x_min[i]);
                if (x[i] < x_min[i]) {
                    ok = false;
                    break;
                }
            }
            if (!ok) {
                left = mid;
                continue;
            }
            if (x[0] > k) {
                left = mid;
            } else {
                right = mid;
            }
        }
        double final_V = right;
        vector<int> final_x(n);
        for (int i = 0; i < n; i++) {
            if (final_V >= a[i]) {
                final_x[i] = 0;
            } else {
                double ratio = a[i] / final_V;
                final_x[i] = ceil(log2(ratio));
            }
        }
        final_x.back() = 0;
        for (int i = n - 2; i >= 0; i--) {
            final_x[i] = min(final_x[i + 1], final_x[i]);
        }
        int max_x = 0;
        double max_val = 0;
        for (int i = 0; i < n; i++) {
            int xi = final_x[i];
            double val = a[i] / (1LL << xi);
            if (val > max_val) {
                max_val = val;
            }
        }
        i64 numerator = 0;
        int exponent = 0;
        while (true) {
            i64 candidate = round(max_val * (1LL << exponent));
            if (abs(candidate / (double)(1LL << exponent) - max_val) < 1e-9) {
                numerator = candidate;
                break;
            }
            exponent++;
            if (exponent > 60) break;
        }
        while (exponent > 0 && (numerator % 2 == 0)) {
            numerator /= 2;
            exponent--;
        }
        string s;
        if (numerator == 0) {
            s = "0";
        } else {
            while (numerator > 0) {
                s += (numerator % 2) + '0';
                numerator /= 2;
            }
            reverse(s.begin(), s.end());
        }
        cout << s << '\n';
    }
}