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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;

public class Codeforces {

    static double Phi = (1 + Math.sqrt(5)) / 2.0;
    static int MAX = -1 >>> 1;
    static long MODL = 1_000_000_007L;
    static int MOD = 1_000_000_007;
    static void no() throws IOException {println("NO");}
    static void yes() throws IOException {println("YES");}

    static boolean testCases = true;
    static boolean DEBUG = true;

    static void main() throws Exception {
        int n = ni();
        long k = nl();
        // 1 <= k <= n2
        String s = line();
        int[] c = new int[n];
        Queue<Integer> q = new LinkedList<>();
        for (int i = 0; i < n; ++i) {
            if (s.charAt(i) == '0') {
                c[i] = 0;
                q.add(i);
            } else {
                c[i] = 1;
            }
        }
        int prevZeroIndex = -1;
        while (!q.isEmpty()) {
            int index = q.poll();
            long[] res = move(c, prevZeroIndex, index, k);
            k = res[0];
            prevZeroIndex = (int) res[1];
        }
        StringBuilder sb = new StringBuilder(n);
        for (int ele : c) {
            sb.append(ele);
        }
        println(sb.toString());
    }
    static long[] move(int[] c, int prev, int index, long moves) {
        long pos;
        if (index - prev - 1 <= moves) {
            pos = prev + 1;
            moves -= index - prev - 1;
        } else {
            pos = index - moves;
            moves = 0;
        }
        c[index] = 1;
        c[(int) pos] = 0;
        return new long[] {moves, pos};
    }
    public static void main(String[] args) throws Exception {
        long startPointTime = System.currentTimeMillis();
        scannerIn = System.in;
        printerBW = new BufferedWriter(new OutputStreamWriter(System.out));
        if (DEBUG && System.getProperty("ONLINE_JUDGE") == null) {
            HABLA = true;
            debug("Debugging enabled");
        }

        int t = testCases ? ni() : 1;
        int to = t;
        while (t-- > 0) {
            debug("Case #" + (to - t) + " ---------------- ");
            main();
        }
        long endTime = System.currentTimeMillis();
        float totalProgramTime = endTime - startPointTime;
        if (HABLA)
            debug("Execution time is " + totalProgramTime + " (" + (totalProgramTime / 1000) + "s)");
        close();
    }

//IO Stuff
    private static boolean HABLA = false;
    private static byte[] scannerByteBuffer = new byte[1024]; // Buffer of Bytes
    private static int scannerIndex;
    private static InputStream scannerIn;
    private static int scannerTotal;
    private static BufferedWriter printerBW;

    private static int next() throws IOException { // Scan method used to scan buf
        if (scannerTotal < 0)
            throw new InputMismatchException();
        if (scannerIndex >= scannerTotal) {
            scannerIndex = 0;
            scannerTotal = scannerIn.read(scannerByteBuffer);
            if (scannerTotal <= 0)
                return -1;
        }
        return scannerByteBuffer[scannerIndex++];
    }

    static int ni() throws IOException {
        int integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static long nl() throws IOException {
        long integer = 0;
        int n = next();
        while (isWhiteSpace(n)) // Removing startPointing whitespaces
            n = next();
        int neg = 1;
        if (n == '-') { // If Negative Sign encounters
            neg = -1;
            n = next();
        }
        while (!isWhiteSpace(n)) {
            if (n >= '0' && n <= '9') {
                integer *= 10;
                integer += n - '0';
                n = next();
            } else
                throw new InputMismatchException();
        }
        return neg * integer;
    }

    static String line() throws IOException {
        StringBuilder sb = new StringBuilder();
        int n = next();
        while (isWhiteSpace(n))
            n = next();
        while (!isNewLine(n)) {
            sb.append((char) n);
            n = next();
        }
        return sb.toString();
    }

    private static boolean isNewLine(int n) {
        return n == '\n' || n == '\r' || n == -1;
    }

    private static boolean isWhiteSpace(int n) {
        return n == ' ' || isNewLine(n) || n == '\t';
    }

    static int[] nia(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        int[] array = new int[n];
        for (int i = 0; i < n; i++)
            array[i] = ni();
        return array;
    }

    static long[] nla(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static float[] nfa(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        float[] array = new float[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static double[] nda(int n) throws Exception {
        if (n < 0)
            throw new Exception("Array size should be non negative");
        double[] array = new double[n];
        for (int i = 0; i < n; i++)
            array[i] = nl();
        return array;
    }

    static <T> void print(T str) throws IOException {
        printerBW.append(str.toString());
        if (HABLA) flush();
    }

    static <T> void println() throws IOException {
        printerBW.append('\n');
        if (HABLA) flush();
    }

    static <T> void println(T str) throws IOException {
        if (str == null) {
            printerBW.append("null\n");
        } else {
            printerBW.append(str.toString());
            printerBW.append('\n');
            if (HABLA) flush();
        }
    }

    public static final String ANSI_RESET = "\u001B[0m";
    public static final String ANSI_DEBUG = "\u001B[33m";
    static <T> void debugl(T str) throws IOException {
        if (!HABLA) return;
        if (str == null) {
            printerBW.append(ANSI_DEBUG);
            printerBW.append("null");
            printerBW.append(ANSI_RESET);
        } else {
            printerBW.append(ANSI_DEBUG);
            printerBW.append(str.toString());
            printerBW.append(ANSI_RESET);
        }
        flush();
    }

    static void debug() throws IOException {
        if (!HABLA) return;
        printerBW.append('\n');
        flush();
    }
    static <T> void debug(T str) throws IOException {
        if (!HABLA) return;
        if (str == null) {
            printerBW.append(ANSI_DEBUG);
            printerBW.append("null\n");
            printerBW.append(ANSI_RESET);
        } else {
            printerBW.append(ANSI_DEBUG);
            printerBW.append(str.toString());
            printerBW.append(ANSI_RESET);
            printerBW.append('\n');
        }
        flush();
    }

    static void flush() throws IOException {
        printerBW.flush();
    }

    static void close() {
        try {
            printerBW.close();
        } catch (IOException e) {
            System.out.println(e.toString());
        }
    }
}
