Problem: This is an interactive problem.

Ayush devised a new scheme to set the password of his lock. The lock has k slots where each slot can hold integers from 1 to n. The password P is a sequence of k integers each in the range [1, n], i-th element of which goes into the i-th slot of the lock.

To set the password of his lock, Ayush comes up with an array A of n integers each in the range [1, n] (not necessarily distinct). He then picks k non-empty mutually disjoint subsets of indices S_1, S_2, ..., S_k (S_i \underset{i ≠ j} ∩ S_j = ∅) and sets his password as P_i = max_{j ∉ S_i} A[j]. In other words, the i-th integer in the password is equal to the maximum over all elements of A whose indices do not belong to S_i.

You are given the subsets of indices chosen by Ayush. You need to guess the password. To make a query, you can choose a non-empty subset of indices of the array and ask the maximum of all elements of the array with index in this subset. You can ask no more than 12 queries.

Input

The first line of the input contains a single integer t (1 ≤ t ≤ 10) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers n and k (2 ≤ n ≤ 1000, 1 ≤ k ≤ n) — the size of the array and the number of subsets. k lines follow. The i-th line contains an integer c (1 ≤ c < n) — the size of subset S_i, followed by c distinct integers in the range [1, n] — indices from the subset S_i.

It is guaranteed that the intersection of any two subsets is empty.

Interaction

To ask a query print a single line: 

  * In the beginning print "? c " (without quotes) where c (1 ≤ c ≤ n) denotes the size of the subset of indices being queried, followed by c distinct space-separated integers in the range [1, n]. 



For each query, you will receive an integer x — the maximum of value in the array among all the indices queried. If the subset of indices queried is invalid or you exceeded the number of queries (for example one of the indices is greater than n) then you will get x = -1. In this case, you should terminate the program immediately.

When you have guessed the password, print a single line "! " (without quotes), followed by k space-separated integers — the password sequence.

Guessing the password does not count towards the number of queries asked.

After this, you should read a string. If you guess the password correctly, you will receive the string "Correct". In this case, you should continue solving the remaining test cases. If the guessed password is incorrect, you will receive the string "Incorrect". In this case, you should terminate the program immediately.

The interactor is not adaptive. The array A does not change with queries.

After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * see documentation for other languages.



Hacks

To hack the solution use the following test format:

The first line of the input should contain a single integer t (1 ≤ t ≤ 10) — the number of test cases. 

The first line of each test case should contain two integers n and k (2 ≤ n ≤ 1000, 1 ≤ k ≤ n) — the size of the array and the number of subsets. The next line should consist of n space separated integers in the range [1, n] — the array A. k lines should follow. The i-th line should contain an integer c (1 ≤ c < n) — the size of subset S_i, followed by c distinct integers in the range [1, n] — indices from the subset S_i.

The intersection of any two subsets has to be empty.

Example

Input


1
4 2
2 1 3
2 2 4

1

2

3

4

Correct

Output


? 1 1

? 1 2

? 1 3

? 1 4

! 4 3

Note

The array A in the example is [1, 2, 3, 4]. The length of the password is 2. The first element of the password is the maximum of A[2], A[4] (since the first subset contains indices 1 and 3, we take maximum over remaining indices). The second element of the password is the maximum of A[1], A[3] (since the second subset contains indices 2, 4).

Do not forget to read the string "Correct" / "Incorrect" after guessing the password.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;

 
public class Main {
	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		InputReader in = new InputReader(inputStream);
		
//		for(int i=4;i<=4;i++) {
//			InputStream uinputStream = new FileInputStream("timeline.in");
			//String f = i+".in";
			//InputStream uinputStream = new FileInputStream(f);
//			InputReader in = new InputReader(uinputStream);
//			PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("timeline.out")));
//		}
		Task t = new Task();
		t.solve(in, out);
		out.close();
	}	
	
	static class Task{

		public void solve(InputReader in, PrintWriter out) throws IOException {
			int c = in.nextInt();
			while(c-->0) {
				int n = in.nextInt();
				int k = in.nextInt();
				ArrayList<Integer>[] g = new ArrayList[n];
				for(int i=0;i<n;i++) g[i] = new ArrayList<Integer>();
				for(int i=0;i<k;i++) {
					int num = in.nextInt();
					for(int j=0;j<num;j++) {
						g[i].add(in.nextInt());
					}
				}
				StringBuilder ret = new StringBuilder();
				ret.append("!");
				if(k<=12) {
					for(int i=0;i<k;i++) {
						Set<Integer> all = new HashSet<Integer>();
						for(int j=1;j<=n;j++) all.add(j);
						for(int j:g[i]) all.remove(j);
						StringBuilder sb = new StringBuilder();
						sb.append("? ").append(all.size());
						for(int j:all) {
							sb.append(" ").append(j);
						}
						out.println(sb.toString());
						out.flush();
						int m = in.nextInt();						
						ret.append(" ").append(m);
					}
				}else {
					Set<Integer> all = new HashSet<Integer>();
					for(int j=1;j<=n;j++) all.add(j);
					StringBuilder sb = new StringBuilder();
					sb.append("? ").append(all.size());	
					for(int j:all) {
						sb.append(" ").append(j);
					}
					out.println(sb.toString());
					out.flush();
					int max = in.nextInt();	
					
					int l = 0; int r = k-1;				
					while(l<r) {
						int mid = l+(r-l)/2;
						String ql = query(g,l,mid);
						out.println(ql);
						out.flush();
						int ml = in.nextInt();
						if(ml==max) {
							r=mid;
						}else {
							l=mid+1;
						}
					}

						all = new HashSet<Integer>();
						for(int j=1;j<=n;j++) all.add(j);
						for(int j:g[l]) all.remove(j);
						sb = new StringBuilder();
						sb.append("? ").append(all.size());	
						for(int j:all) {
							sb.append(" ").append(j);
						}
						out.println(sb.toString());
						out.flush();
						int max2 = in.nextInt();	
						for(int i=0;i<k;i++) {
							ret.append(" ");
							ret.append(i==l?max2:max);
						}
				}
				out.println(ret.toString());
				out.flush();
				String result = in.next();
				if(!result.equals("Correct")) {
					break;
				}
			}
		}
		String query(ArrayList<Integer>[] g, int f, int t) {
			int n = 0;
			for(int i=f;i<=t;i++) {
				n+=g[i].size();
			}
			StringBuilder sb = new StringBuilder();
			sb.append("? ").append(n);
			for(int i=f;i<=t;i++) {
				for(int j:g[i])
					sb.append(" ").append(j);
			}
			return sb.toString();
		}



	    public double getProbability(int[] balls) {
	        int sum = 0;
	        int col = balls.length;
	        int p = 0;
	        int q = 0;
	        for(int i:balls) sum+=i;
	        int t[] = new int[sum];
	        for(int i:balls) {
	        	for(int j=0;j<i;j++) {
	        		t[q++] = p;
	        	}
	        	p++;
	        }
	        int cnt[][] = new int[col+1][sum+1];
	        int cnt2[][] = new int[col+1][sum+1];
	        for(int i=1;i<1<<sum/2;i++) {
	        	int num = 0;
	        	int hash1[] = new int[10];
	        	int hash2[] = new int[10];
	        	for(int j=0;j<sum/2;j++) {
	        		if((i&(1<<j))!=0) {
	        			num++;
	        			hash1[t[sum/2-1-j]] = 1;
	        			hash2[t[sum-1-j]] = 1;
	        		}
	        	}
	        	p=0;q=0;
	        	for(int j:hash1) p+=j;
	        	for(int j:hash2) q+=j;
	        	cnt[num][p]++;	        	
	        	cnt2[num][q]++;
	        }
	        int ret = 0;
	        for(int i=col/2;i<=Math.min(col, sum/2);i++) {
	        	for(int j=0;j<=sum/2;j++) {	        		
	        		ret+=cnt[i][j]*cnt[i][sum/2-j];
	        	}
	        }
	        int f[] = new int[col];
	        for(int i=0;i<col;i++) {
	        	int x = 1;
	        	for(int j=2;j<=balls[i];j++) {
	        		x*=j;
	        	}
	        	f[i] = x;
	        }
	        int tot = 1;
	        p = 0;
	        for(int i=sum;i>=1;i--) {
	        	tot*=i;
	        	if(p<col&&tot>=f[p]) tot/=f[p++];
	        }
	        return 1.0*ret/tot;
	    }    


	    long longRandomPrime() {
	        BigInteger prime = BigInteger.probablePrime(31, new Random());
	        return prime.longValue();
	    }
		
		static class lca_naive{
			int n;
			ArrayList<edge>[] g;
			int lvl[];
			int pare[];
			int dist[];
			public lca_naive(int t, ArrayList<edge>[] x) {
				n=t;
				g=x; 
				lvl = new int[n];
				pare = new int[n];
				dist = new int[n];
			}
			void pre_process() {
				dfs(0,-1,g,lvl,pare,dist);
			}
			void dfs(int cur, int pre, ArrayList<edge>[] g, int lvl[], int pare[], int dist[]) {
				for(edge nxt_edge:g[cur]) {
					if(nxt_edge.t!=pre) {
						lvl[nxt_edge.t] = lvl[cur]+1;
						dist[nxt_edge.t] = dist[cur]+nxt_edge.len;
						pare[nxt_edge.t] = cur;
						dfs(nxt_edge.t,cur,g,lvl,pare,dist);
					}
				}				
			}
			public int work(int p, int q) {
				int a = p;
				int b = q;
				while(lvl[p]<lvl[q]) q = pare[q];
				while(lvl[p]>lvl[q]) p = pare[p];			
				while(p!=q){p = pare[p]; q = pare[q];}
				int c = p;
				return dist[a]+dist[b]-dist[c]*2;
			}
		}
		static class lca_binary_lifting{
			int n;
			ArrayList<edge>[] g;
			int lvl[];
			int pare[];
			int dist[];
			int table[][];
			public lca_binary_lifting(int a, ArrayList<edge>[] t) {
				n = a;
				g = t;
				lvl = new int[n];
				pare = new int[n];
				dist = new int[n];				
				table = new int[20][n];				
			}
			void pre_process() {
				dfs(0,-1,g,lvl,pare,dist);
				for(int i=0;i<20;i++) {
					for(int j=0;j<n;j++) {
						if(i==0) table[0][j] = pare[j];
						else table[i][j] = table[i-1][table[i-1][j]];
					}
				}				
			}
			void dfs(int cur, int pre, ArrayList<edge>[] g, int lvl[], int pare[], int dist[]) {
				for(edge nxt_edge:g[cur]) {
					if(nxt_edge.t!=pre) {
						lvl[nxt_edge.t] = lvl[cur]+1;
						dist[nxt_edge.t] = dist[cur]+nxt_edge.len;
						pare[nxt_edge.t] = cur;
						dfs(nxt_edge.t,cur,g,lvl,pare,dist);
					}
				}				
			}			
			public int work(int p, int q) {
				int a = p;
				int b = q;
				if(lvl[p]>lvl[q]) {
					int tmp = p;
					p=q;
					q=tmp;
				}				
				for(int i=19;i>=0;i--) {
					if(lvl[table[i][q]]>=lvl[p]) q=table[i][q];
				}				
				if(p==q) return p;// return dist[a]+dist[b]-dist[p]*2;
				for(int i=19;i>=0;i--) {
					if(table[i][p]!=table[i][q]) {
						p = table[i][p];
						q = table[i][q];
					}
				}
				return table[0][p];
				//return dist[a]+dist[b]-dist[table[0][p]]*2;
			}
		}
		static class lca_sqrt_root{
			int n;
			ArrayList<edge>[] g;
			int lvl[];
			int pare[];
			int dist[];
			int jump[];
			int sz;
			public lca_sqrt_root(int a, ArrayList<edge>[] b) {
				n=a;
				g=b;
				lvl = new int[n];
				pare = new int[n];
				dist = new int[n];
				jump = new int[n];
				sz = (int) Math.sqrt(n);
			}
			void pre_process() {
				dfs(0,-1,g,lvl,pare,dist,jump);
			}
			void dfs(int cur, int pre, ArrayList<edge>[] g, int lvl[], int pare[], int dist[], int[] jump) {
				for(edge nxt_edge:g[cur]) {
					if(nxt_edge.t!=pre) {
						lvl[nxt_edge.t] = lvl[cur]+1;
						dist[nxt_edge.t] = dist[cur]+nxt_edge.len;
						pare[nxt_edge.t] = cur;
						if(lvl[nxt_edge.t]%sz==0) {
							jump[nxt_edge.t] = cur;
						}else {
							jump[nxt_edge.t] = jump[cur];
						}
						dfs(nxt_edge.t,cur,g,lvl,pare,dist,jump);
					}
				}				
			}
			int work(int p, int q) {
				int a = p; int b = q;
				if(lvl[p]>lvl[q]) {
					int tmp = p;
					p=q;
					q=tmp;
				}
				while(jump[p]!=jump[q]) {
					if(lvl[p]>lvl[q]) p = jump[p];
					else q = jump[q];
				}
				while(p!=q) {
					if(lvl[p]>lvl[q]) p = pare[p];
					else q = pare[q];
				}
				return dist[a]+dist[b]-dist[p]*2;
			}
		}
		
		class edge implements Comparable<edge>{
			int f,t,len;
			public edge(int a, int b, int c) {
				f=a;t=b;len=c;
			}
			@Override
			public int compareTo(edge t) {				
				return t.len-this.len;
			}
		}
	
		class pair implements Comparable<pair>{
			int idx,lvl;
			public pair(int a, int b) {
				idx = a;
				lvl = b;
			}
			@Override
			public int compareTo(pair t) {
				return t.lvl-this.lvl;
			}
		}		
		
		static class lca_RMQ{
			int n;
			ArrayList<edge>[] g;
			int lvl[];
			int dist[];
			int tour[];
			int tour_rank[];
			int first_occ[];
			int c;
			sgt s;
			public lca_RMQ(int a, ArrayList<edge>[] b) {
				n=a;
				g=b;
				c=0;
				lvl = new int[n];
				dist = new int[n];
				tour = new int[2*n];
				tour_rank = new int[2*n];
				first_occ = new int[n];
				Arrays.fill(first_occ, -1);
			}
			void pre_process() {
				tour[c++] = 0;
				dfs(0,-1);
				for(int i=0;i<2*n;i++) {
					tour_rank[i] = lvl[tour[i]];
					if(first_occ[tour[i]]==-1) first_occ[tour[i]] = i;
				}
				s = new sgt(0,2*n,tour_rank);
			}
			void dfs(int cur, int pre) {
				for(edge nxt_edge:g[cur]) {
					if(nxt_edge.t!=pre) {
						lvl[nxt_edge.t] = lvl[cur]+1;
						dist[nxt_edge.t] = dist[cur]+nxt_edge.len;
						tour[c++] = nxt_edge.t;
						dfs(nxt_edge.t,cur);
						tour[c++] = cur;
					}
				}				
			}			
			int work(int p,int q) {			
				int a = Math.max(first_occ[p], first_occ[q]);
				int b = Math.min(first_occ[p], first_occ[q]);
				int idx = s.query_min_idx(b, a+1);
				//Dumper.print(a+" "+b+" "+idx);
				int c = tour[idx];
				return dist[p]+dist[q]-dist[c]*2;
			}
		}		

		  
	    static class sgt{
	    	sgt lt;
	    	sgt rt;
	    	int l,r;
	    	int sum, max, min, lazy;
	    	int min_idx;
	    	public sgt(int L, int R, int arr[]) {
	    		l=L;r=R;
	    		if(l==r-1) {
	    			sum = max = min = arr[l];
	    			lazy = 0;
	    			min_idx = l;
	    			return;
	    		}
	    		lt = new sgt(l, l+r>>1, arr);
	    		rt = new sgt(l+r>>1, r, arr);
	    		pop_up();
	    	}
	    	void pop_up() {
	    		this.sum = lt.sum + rt.sum;
	    		this.max = Math.max(lt.max, rt.max);
	    		this.min = Math.min(lt.min, rt.min);
	    		if(lt.min<rt.min)
	    			this.min_idx = lt.min_idx;
	    		else if(lt.min>rt.min) this.min_idx = rt.min_idx;
	    		else this.min = Math.min(lt.min_idx, rt.min_idx);
	    	}
	    	void push_down() {
	    		if(this.lazy!=0) {
	    			lt.sum+=lazy;
	    			rt.sum+=lazy;
	    			lt.max+=lazy;
	    			lt.min+=lazy;
	    			rt.max+=lazy;
	    			rt.min+=lazy;
	    			lt.lazy+=this.lazy;
	    			rt.lazy+=this.lazy;
	    			this.lazy = 0;
	    		}
	    	}
	    	void change(int L, int R, int v) {
	    		if(R<=l||r<=L) return;
	    		if(L<=l&&r<=R) {
	    			this.max+=v;
	    			this.min+=v;
	    			this.sum+=v*(r-l);
	    			this.lazy+=v;
	    			return;
	    		}
	    		push_down();
	    		lt.change(L, R, v);
	    		rt.change(L, R, v);
	    		pop_up();
	    	}
	    	int query_max(int L, int R) {
	    		if(L<=l&&r<=R) return this.max;
	    		if(r<=L||R<=l) return Integer.MIN_VALUE;
	    		push_down();
	    		return Math.max(lt.query_max(L, R), rt.query_max(L, R));	    		
	    	}
	    	int query_min(int L, int R) {
	    		if(L<=l&&r<=R) return this.min;
	    		if(r<=L||R<=l) return Integer.MAX_VALUE;
	    		push_down();
	    		return Math.min(lt.query_min(L, R), rt.query_min(L, R));	
	    	}
	    	int query_sum(int L, int R) {
	    		if(L<=l&&r<=R) return this.sum;
	    		if(r<=L||R<=l) return 0;
	    		push_down();
	    		return lt.query_sum(L, R) + rt.query_sum(L, R);
	    	}
	    	int query_min_idx(int L, int R) {
	    		if(L<=l&&r<=R) return this.min_idx;
	    		if(r<=L||R<=l) return Integer.MAX_VALUE;
	    		int a = lt.query_min_idx(L, R);
	    		int b = rt.query_min_idx(L, R);
	    		int aa = lt.query_min(L, R);
	    		int bb = rt.query_min(L, R);
	    		if(aa<bb) return a;
	    		else if(aa>bb) return b;	    		
	    		return Math.min(a,b);
	    	}
	    }	   
			    	
		List<List<Integer>> convert(int arr[][]){
			int n = arr.length;
			List<List<Integer>> ret = new ArrayList<>();
			for(int i=0;i<n;i++) {
				ArrayList<Integer> tmp = new ArrayList<Integer>();
				for(int j=0;j<arr[i].length;j++) tmp.add(arr[i][j]);
				ret.add(tmp);
			}
			return ret;
		}
		
		public class TreeNode {
			int val;
			TreeNode left;
			TreeNode right;
			TreeNode(int x) { val = x; }
		}
	
		public int GCD(int a, int b) {
		   if (b==0) return a;
		   return GCD(b,a%b);
		}
		public long GCD(long a, long b) {
			   if (b==0) return a;
			   return GCD(b,a%b);
		}		
	}
	
	
    static class ArrayUtils {
        static final long seed = System.nanoTime();
        static final Random rand = new Random(seed);
 
        public static void sort(int[] a) {
            shuffle(a);
            Arrays.sort(a);
        }
 
        public static void shuffle(int[] a) {
            for (int i = 0; i < a.length; i++) {
                int j = rand.nextInt(i + 1);
                int t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
        }
        
        public static void sort(long[] a) {
            shuffle(a);
            Arrays.sort(a);
        }        
        
        public static void shuffle(long[] a) {
            for (int i = 0; i < a.length; i++) {
                int j = rand.nextInt(i + 1);
                long t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
        }
    }	
	static class BIT{
		int arr[];
		int n;
		public BIT(int a) {
			n=a;
			arr = new int[n];
		}
		int sum(int p) {
			int s=0;
			while(p>0) {
				s+=arr[p];
				p-=p&(-p);
			}
			return s;
		}
		void add(int p, int v) {
			while(p<n) {
				arr[p]+=v;
				p+=p&(-p);
			}
		}
	}
	static class DSU{
		int[] arr;
		int[] sz;
		public DSU(int n) {
			arr = new int[n];
			sz = new int[n];
			for(int i=0;i<n;i++) arr[i] = i;
			Arrays.fill(sz, 1);
		}
		public int find(int a) {
			if(arr[a]!=a) arr[a] = find(arr[a]);
			return arr[a];
		}
		public void union(int a, int b) {
			int x = find(a);
			int y = find(b);
			if(x==y) return;
			arr[y] = x;
			sz[x] += sz[y];
		}
		public int size(int x) {
			return sz[find(x)];
		}
	}	
	static class MinHeap<Key> implements Iterable<Key> {
		private int maxN;
		private int n;
		private int[] pq;
		private int[] qp;
		private Key[] keys;
		private Comparator<Key> comparator;
		
		public MinHeap(int capacity){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
		}
		
		public MinHeap(int capacity, Comparator<Key> c){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
			comparator = c;
		}			
		public boolean isEmpty()	{ return n==0; 	}
		public int size()			{ return n;		}
		public boolean contains(int i) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        return qp[i] != -1;
		}	
		public int peekIdx() {
	        if (n == 0) throw new NoSuchElementException("Priority queue underflow");
	        return pq[1];		
		}	
		public Key peek(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			return keys[pq[1]];
		}
		public int poll(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			int min = pq[1];
			exch(1,n--);
			down(1);
			assert min==pq[n+1];
			qp[min] = -1;
			keys[min] = null;		
			pq[n+1] = -1;
			return min;
		}
	    public void update(int i, Key key) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (!contains(i)) {
	        	this.add(i, key);
	        }else {
	        	keys[i] = key;
	        	up(qp[i]);
	        	down(qp[i]);
	        }
	    }	
		private void add(int i, Key x){
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (contains(i)) throw new IllegalArgumentException("index is already in the priority queue");
	        n++;
	        qp[i] = n;
	        pq[n] = i;
	        keys[i] = x;
	        up(n);
		}
		private void up(int k){
			while(k>1&&less(k,k/2)){
				exch(k,k/2);
				k/=2;
			}
		}
		private void down(int k){
			while(2*k<=n){
				int j=2*k;
				if(j<n&&less(j+1,j)) j++;
				if(less(k,j)) break;
				exch(k,j);
				k=j;
			}
		}
		
		public boolean less(int i, int j){
	        if (comparator == null) {
	            return ((Comparable<Key>) keys[pq[i]]).compareTo(keys[pq[j]]) < 0;
	        }
	        else {
	            return comparator.compare(keys[pq[i]], keys[pq[j]]) < 0;
	        }
		}
 
		public void exch(int i, int j){
	        int swap = pq[i];
	        pq[i] = pq[j];
	        pq[j] = swap;
	        qp[pq[i]] = i;
	        qp[pq[j]] = j;
		}
 
		@Override
		public Iterator<Key> iterator() {
			// TODO Auto-generated method stub
			return null;
		}
	}  	
 
    private static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int zcurChar;
        private int znumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }
 
        public int read()
        {
            if (znumChars == -1)
                throw new InputMismatchException();
            if (zcurChar >= znumChars)
            {
            	zcurChar = 0;
                try
                {
                    znumChars = stream.read(buf);
                } catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (znumChars <= 0)
                    return -1;
            }
            return buf[zcurChar++];
        }
 
        public int nextInt()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public String nextString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public String next()
        {
            return nextString();
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
        public int[] readIntArray(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }        
    }    
 
	static class Dumper {
		static void print_int_arr(int[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}
 
		static void print_char_arr(char[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}
 
		static void print_double_arr(double[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}
 
		static void print_2d_arr(int[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}
 
		static void print_2d_arr(boolean[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}
 
		static void print(Object o) {
			System.out.println(o.toString());
		}
 
		static void getc() {
			System.out.println("here");
		}
	}
}