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.
import java.io.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
import static java.util.Comparator.*;

public class Main {
    FastScanner in;
    PrintWriter out;
    ArrayList<Integer>[] graph;
    ArrayList<GraphPair>[] weightedGraph;
    long mod = (long) 1e9 + 7; // 998_244_353L || (long) 1e9 + 9
    boolean multitests = true;

    private void solve() throws IOException {
        // solveA();
        // solveB();
        // solveC();
        solveD();
        // solveE();
        // solveF();
    }

    private void solveA() throws IOException {
        long a = in.nextLong(), b = in.nextLong(), n = in.nextLong(), S = in.nextLong();
        out.println(S % n <= b && n * a + b >= S ? "YES" : "NO");
    }

    private void solveB() throws IOException {
        int n = in.nextInt();
        int[] p = in.nextIntArray(n);

        boolean[] used = new boolean[n + 1];
        for (int l = 0, r = 0, next = 1; l < n; l = r) {
            while (p[r] != next)
                r++;

            if (l == r) {
                used[next++] = true;
                r++;
            } else {
                for (int i = r; i > l; i--)
                    p[i] = p[i - 1];
                p[l] = next++;
                for (int i = l; i < r; i++)
                    used[p[i]] = true;
            }
            while (next <= n && used[next])
                next++;
        }

        for (int i = 0; i < n; i++)
            out.print(p[i] + " ");
        out.println();
    }

    private void solveC() throws IOException {
        int n = in.nextInt(), m = in.nextInt(), d = in.nextInt();
        int[] c = in.nextIntArray(m);
        int sum = (int) sumInt(c);
        if ((d - 1) * (m + 1) + sum >= n) {
            out.println("YES");
            int zero = n - sum;
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < d - 1 && zero-- > 0; j++)
                    out.print("0 ");
                for (int j = 0; j < c[i]; j++)
                    out.print(i + 1 + " ");
            }
            while (zero-- > 0)
                out.print("0 ");
        } else {
            out.println("NO");
        }
    }

    private void solveD() throws IOException {
        int n = in.nextInt();
        long k = in.nextLong();
        char[] s = in.next().toCharArray();

        long cnt = 0, sum = 0;
        for (int i = 0; i < n; i++) {
            if (s[i] == '0') {
                sum += cnt;

                if (sum > k) {
                    sum -= cnt;

                    char[] ans = new char[n];
                    for (int j = 0; j < i - cnt; j++)
                        ans[j] = '0';
                    for (int j = 0; j < cnt; j++)
                        ans[i - (int) cnt + j] = '1';
                    ans[i] = '0';
                    for (int j = i + 1; j < n; j++)
                        ans[j] = s[j];

                    for (int j = i; sum++ < k; j--) {
                        ans[j] = '1';
                        ans[j - 1] = '0';
                    }

                    out.println(new String(ans));
                    return;
                }

            } else
                cnt++;
        }

        for (int i = 0; i < n - cnt; i++)
            out.print("0");
        for (int i = 0; i < cnt; i++)
            out.print("1");
        out.println();
    }

    private void solveE() throws IOException {

    }

    private void solveF() throws IOException {

    }

    void shuffleInt(int[] a) {
        Random random = new Random();
        for (int i = a.length - 1; i > 0; i--) {
            int j = random.nextInt(i + 1);
            int swap = a[j];
            a[j] = a[i];
            a[i] = swap;
        }
    }

    void shuffleLong(long[] a) {
        Random random = new Random();
        for (int i = a.length - 1; i > 0; i--) {
            int j = random.nextInt(i + 1);
            long swap = a[j];
            a[j] = a[i];
            a[i] = swap;
        }
    }

    void reverseInt(int[] a) {
        for (int i = 0, j = a.length - 1; i < j; i++, j--) {
            int swap = a[i];
            a[i] = a[j];
            a[j] = swap;
        }
    }

    void reverseLong(long[] a) {
        for (int i = 0, j = a.length - 1; i < j; i++, j--) {
            long swap = a[i];
            a[i] = a[j];
            a[j] = swap;
        }
    }

    int maxInt(int[] a) {
        int max = a[0];
        for (int i = 1; i < a.length; i++)
            if (max < a[i])
                max = a[i];
        return max;
    }

    long maxLong(long[] a) {
        long max = a[0];
        for (int i = 1; i < a.length; i++)
            if (max < a[i])
                max = a[i];
        return max;
    }

    int minInt(int[] a) {
        int min = a[0];
        for (int i = 1; i < a.length; i++)
            if (min > a[i])
                min = a[i];
        return min;
    }

    long minLong(long[] a) {
        long min = a[0];
        for (int i = 1; i < a.length; i++)
            if (min > a[i])
                min = a[i];
        return min;
    }

    long sumInt(int[] a) {
        long s = 0;
        for (int i = 0; i < a.length; i++)
            s += a[i];
        return s;
    }

    long sumLong(long[] a) {
        long s = 0;
        for (int i = 0; i < a.length; i++)
            s += a[i];
        return s;
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long binpowmod(long a, long n) {
        long res = 1;
        a %= mod;
        n %= mod - 1;
        while (n > 0) {
            if (n % 2 == 1)
                res = (res * a) % mod;
            a = (a * a) % mod;
            n /= 2;
        }
        return res;
    }

    class GraphPair implements Comparable<GraphPair> {
        int v;
        long w;

        GraphPair(int v, long w) {
            this.v = v;
            this.w = w;
        }

        public int compareTo(GraphPair o) {
            return w != o.w ? Long.compare(w, o.w) : Integer.compare(v, o.v);
        }
    }

    ArrayList<Integer>[] createGraph(int n) throws IOException {
        ArrayList<Integer>[] graph = new ArrayList[n];
        for (int i = 0; i < n; i++)
            graph[i] = new ArrayList<>();
        return graph;
    }

    ArrayList<GraphPair>[] createWeightedGraph(int n) throws IOException {
        ArrayList<GraphPair>[] graph = new ArrayList[n];
        for (int i = 0; i < n; i++)
            graph[i] = new ArrayList<>();
        return graph;
    }

    class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s), 32768);
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        boolean hasNext() throws IOException {
            return br.ready() || (st != null && st.hasMoreTokens());
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextInt();
            return a;
        }

        int[][] nextIntTable(int n, int m) throws IOException {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = in.nextInt();
            return a;
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = in.nextLong();
            return a;
        }

        long[][] nextLongTable(int n, int m) throws IOException {
            long[][] a = new long[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    a[i][j] = in.nextLong();
            return a;
        }

        ArrayList<Integer>[] nextGraph(int n, int m, boolean directed) throws IOException {
            ArrayList<Integer>[] graph = createGraph(n);
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1, u = in.nextInt() - 1;
                graph[v].add(u);
                if (!directed)
                    graph[u].add(v);
            }
            return graph;
        }

        ArrayList<GraphPair>[] nextWeightedGraph(int n, int m, boolean directed) throws IOException {
            ArrayList<GraphPair>[] graph = createWeightedGraph(n);
            for (int i = 0; i < m; i++) {
                int v = in.nextInt() - 1, u = in.nextInt() - 1;
                long w = in.nextLong();
                graph[v].add(new GraphPair(u, w));
                if (!directed)
                    graph[u].add(new GraphPair(v, w));
            }
            return graph;
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        boolean hasNextLine() throws IOException {
            return br.ready();
        }

    }

    private void run() throws IOException {
        in = new FastScanner(System.in); // new FastScanner(new FileInputStream(".in"));
        out = new PrintWriter(System.out); // new PrintWriter(new FileOutputStream(".out"));

        for (int t = multitests ? in.nextInt() : 1; t-- > 0; )
            solve();

        out.flush();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}