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.*;

public class tr1 {
	static PrintWriter out;
	static StringBuilder sb;
	static int inf = (int) 1e9;
	static long mod = (long) 1e9 + 7;
	static int[] si;
	static ArrayList<Integer> primes;
	static HashSet<Integer> pr;
	static int n, k, m;
	static int[] in;
	static HashMap<Integer, Integer> factors;
	static HashSet<Integer> f;
	static int[] fac, a, b;
	static int[] l, r;
	static int[][] memo;
	static int[] numc;
	static ArrayList<Integer>[] ad;
	static HashMap<Integer, Integer> hm;
	static pair[] ed;
	static TreeSet<Integer>[] np;
	static TreeMap<pair, Integer> tm;
	static int[] ans, h1, h2;
	static char[] h;
	static pair[] mm;
	static boolean[] vis;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out); 
	    int t=sc.nextInt();
	  while(t-->0) {
		  int n=sc.nextInt();
		  long k=sc.nextLong();
		  String s=sc.nextLine();
		  int o=0;
		  sb=new StringBuilder();
		  for(int i=0;i<n;i++) {
			  if(s.charAt(i)=='0') {
				  if(o>=k)
				  {
					  for(int u=0;u<o-k;u++)
						  sb.append('1');
					  sb.append('0');
					  for(int u=0;u<k;u++)
						  sb.append('1');
					  for(int j=i+1;j<n;j++)
						  sb.append(s.charAt(j));
					  k=0;
					  break;
				  }
				  else {
					  sb.append('0');
					  k-=o;
				  }
			  }
			  else
				  o++;
		  }
		  if(k>0) {
			  for(int p=0;p<o;p++)
				  sb.append('1');
		  }
		  out.println(sb);
	  }
		out.flush();
	}
	
	static class pair implements Comparable<pair> {
		int x;
		int y;
        int z;
 		pair(int f, int t,int u) {
			x = f;
			y = t;
			z=u;
			// num = n;
		}

		public String toString() {
			return x + " " + y+" "+z;
		}

		@Override
		public int compareTo(pair o) {
			if(x==o.x)
				if(y==o.y)
					return z-o.z;
				else
					return o.y-y;
			return x-o.x;
		}
	}

	
	static public class FenwickTree { // one-based DS

		int n;
		int[] ft;

		FenwickTree(int size) {
			n = size;
			ft = new int[n + 1];
		}

		int rsq(int b) // O(log n)
		{
			int sum = 0;
			while (b > 0) {
				sum += ft[b];
				b -= b & -b;
			} // min?
			return sum;
		}

		int rsq(int a, int b) {
			return rsq(b) - rsq(a - 1);
		}

		void point_update(int k, int val) // O(log n), update = increment
		{
			while (k <= n) {
				ft[k] += val;
				k += k & -k;
			} // min?
		}

		int point_query(int idx) // c * O(log n), c < 1
		{
			int sum = ft[idx];
			if (idx > 0) {
				int z = idx ^ (idx & -idx);
				--idx;
				while (idx != z) {
					sum -= ft[idx];
					idx ^= idx & -idx;
				}
			}
			return sum;
		}

		void scale(int c) {
			for (int i = 1; i <= n; ++i)
				ft[i] *= c;
		}

		int findIndex(int cumFreq) {
			int msk = n;
			while ((msk & (msk - 1)) != 0)
				msk ^= msk & -msk; // msk will contain the MSB of n

			int idx = 0;
			while (msk != 0) {
				int tIdx = idx + msk;
				if (tIdx <= n && cumFreq >= ft[tIdx]) {
					idx = tIdx;
					cumFreq -= ft[tIdx];
				}
				msk >>= 1;
			}
			if (cumFreq != 0)
				return -1;
			return idx;
		}
	}

	static public class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		long[] array, sTree, lazy;

		SegmentTree(long[] in) {
			array = in;
			N = in.length - 1;
			sTree = new long[N << 1]; // no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new long[N << 1];
			build(1, 1, N);
		}

		void build(int node, int b, int e) // O(n)
		{
			if (b == e)
				sTree[node] = array[b];
			else {
				int mid = b + e >> 1;
				build(node << 1, b, mid);
				build(node << 1 | 1, mid + 1, e);
				sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
			}
		}

		void update_point(int index, int val) // O(log n)
		{
			index += N - 1;
			sTree[index] += val;
			while (index > 1) {
				index >>= 1;
				sTree[index] = sTree[index << 1] + sTree[index << 1 | 1];
			}
		}

		void update_range(int i, int j, long val) // O(log n)
		{
			update_range(1, 1, N, i, j, val);
		}

		void update_range(int node, int b, int e, int i, int j, long val) {
			if (i > e || j < b)
				return;
			if (b >= i && e <= j) {
				sTree[node] += (e - b + 1) * val;
				lazy[node] += val;
			} else {
				int mid = b + e >> 1;
				propagate(node, b, mid, e);
				update_range(node << 1, b, mid, i, j, val);
				update_range(node << 1 | 1, mid + 1, e, i, j, val);
				sTree[node] = sTree[node << 1] + sTree[node << 1 | 1];
			}

		}

		void propagate(int node, int b, int mid, int e) {
			lazy[node << 1] += lazy[node];
			lazy[node << 1 | 1] += lazy[node];
			sTree[node << 1] += (mid - b + 1) * lazy[node];
			sTree[node << 1 | 1] += (e - mid) * lazy[node];
			lazy[node] = 0;
		}

		long query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		long query(int node, int b, int e, int i, int j) // O(log n)
		{
			if (i > e || j < b)
				return 0;
			if (b >= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			propagate(node, b, mid, e);
			long q1 = query(node << 1, b, mid, i, j);
			long q2 = query(node << 1 | 1, mid + 1, e, i, j);
			return q1 + q2;

		}

	}

	static long gcd(long a, long b) {

		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}


	public int[] merge(int[] d, int st, int e) {
		if (st > e)
			return null;
		if (e == st) {
			int[] ans = { d[e] };
			return ans;
		}
		int mid = (st + e) / 2;
		int[] ans = new int[e - st + 1];
		int[] ll = merge(d, st, mid);
		int[] rr = merge(d, mid + 1, e);
		if (ll == null)
			return rr;
		if (rr == null)
			return ll;
		int iver = 0;
		int idxl = 0;
		int idxr = 0;
		for (int i = st; i <= e; i++) {
			if (ll[idxl] < rr[idxr]) {

			}
		}
		return ans;
	}

	public static class pair1 implements Comparable<pair1> {
		int a;
		int idx;

		pair1(int a, int i) {
			this.a = a;
			idx = i;
		}

		public String toString() {
			return a + " " + idx;
		}

		@Override
		public int compareTo(pair1 o) {
			return o.a - a;
		}
	}

	public static class pair2 implements Comparable<pair2> {
		int a;
		int idx;

		pair2(int a, int i) {
			this.a = a;
			idx = i;
		}

		public String toString() {
			return a + " " + idx;
		}

		@Override
		public int compareTo(pair2 o) {
			// TODO Auto-generated method stub
			return idx - o.idx;
		}
	}

	static long inver(long x) {
		int a = (int) x;
		long e = (mod - 2);
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				// System.out.println(res*a);
				res = (int) ((1l * res * a) % mod);
			}
			a = (int) ((1l * a * a) % mod);
			e >>= 1;
		}
		// out.println(res+" "+x);
		return res % mod;
	}

	static int atMostSum(int arr[], int n, int k) {
		int sum = 0;
		int cnt = 0, maxcnt = 0;

		for (int i = 0; i < n; i++) {

			// If adding current element doesn't
			// cross limit add it to current window
			if ((sum + arr[i]) <= k) {
				sum += arr[i];
				cnt++;
			}

			// Else, remove first element of current
			// window and add the current element
			else if (sum != 0) {
				sum = sum - arr[i - cnt] + arr[i];
			}

			// keep track of max length.
			maxcnt = Math.max(cnt, maxcnt);
		}
		return maxcnt;
	}

	public static int[] longestSubarray(int[] inp) {
		// array containing prefix sums up to a certain index i
		int[] p = new int[inp.length];
		p[0] = inp[0];
		for (int i = 1; i < inp.length; i++) {
			p[i] = p[i - 1] + inp[i];
		}

		// array Q from the description below
		int[] q = new int[inp.length];
		q[inp.length - 1] = p[inp.length - 1];
		for (int i = inp.length - 2; i >= 0; i--) {
			q[i] = Math.max(q[i + 1], p[i]);
		}
		int a = 0;
		int b = 0;
		int maxLen = 0;
		int curr;
		int[] res = new int[] { -1, -1 };
		while (b < inp.length) {
			curr = a > 0 ? q[b] - p[a - 1] : q[b];
			if (curr >= 0) {
				if (b - a > maxLen) {
					maxLen = b - a;
					res = new int[] { a, b };
				}
				b++;
			} else {
				a++;
			}
		}
		return res;
	}

	static void factor(int n) {
		if (si[n] == n) {
			f.add(n);
			return;
		}
		f.add(si[n]);
		factor(n / si[n]);
	}

	static void seive() {
		si = new int[100001];
		primes = new ArrayList<>();
		int N = 100001;
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);

		}
	}

	static class unionfind {
		int[] p;
		int[] size;
           int jum;
		unionfind(int n) {
			p = new int[n];
			size = new int[n];

			for (int i = 0; i < n; i++) {
				p[i] = i;
			}
			jum=n;
			Arrays.fill(size, 1);
		}

		int findSet(int v) {
			if (v == p[v])
				return v;
			return p[v] = findSet(p[v]);
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		void combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return;
			jum--;
			if (size[a] > size[b]) {
				p[b] = a;
				size[a] += size[b];

			} else {
				p[a] = b;
				size[b] += size[a];
			}
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

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

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

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

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

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

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}