Problem: Pay attention: this problem is interactive.

Penguin Xoriy came up with a new game recently. He has n icicles numbered from 1 to n. Each icicle has a temperature — an integer from 1 to 109. Exactly two of these icicles are special: their temperature is y, while a temperature of all the others is x ≠ y. You have to find those special icicles. You can choose a non-empty subset of icicles and ask the penguin what is the bitwise exclusive OR (XOR) of the temperatures of the icicles in this subset. Note that you can't ask more than 19 questions.

You are to find the special icicles.

Input

The first line contains three integers n, x, y (2 ≤ n ≤ 1000, 1 ≤ x, y ≤ 109, x ≠ y) — the number of icicles, the temperature of non-special icicles and the temperature of the special icicles.

Output

To give your answer to the penguin you have to print character "!" (without quotes), then print two integers p1, p2 (p1 < p2) — the indexes of the special icicles in ascending order. Note that "!" and p1 should be separated by a space; the indexes should be separated by a space too. After you gave the answer your program should terminate immediately.

Interaction

To ask a question print character "?" (without quotes), an integer c (1 ≤ c ≤ n), and c distinct integers p1, p2, ..., pc (1 ≤ pi ≤ n) — the indexes of icicles that you want to know about. Note that "?" and c should be separated by a space; the indexes should be separated by a space too.

After you asked the question, read a single integer — the answer.

Note that you can't ask more than 19 questions. If you ask more than 19 questions or at least one incorrect question, your solution will get "Wrong answer".

If at some moment your program reads  - 1 as an answer, it should immediately exit (for example, by calling exit(0)). You will get "Wrong answer" in this case, it means that you asked more than 19 questions, or asked an invalid question. If you ignore this, you can get other verdicts since your program will continue to read from a closed stream.

Your solution will get "Idleness Limit Exceeded", if you don't print anything or forget to flush the output, including for the final answer .

To flush you can use (just after printing): 

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



Hacking

For hacking use the following format:

n x y p1 p2

Here 1 ≤ p1 < p2 ≤ n are the indexes of the special icicles.

Contestant programs will not be able to see this input.

Example

Input

4 2 1
2
1
1<span class="tex-font-style-it"></span>

Output

? 3 1 2 3
? 1 1
? 1 3
! 1 3

Note

The answer for the first question is <image>.

The answer for the second and the third questions is 1, therefore, special icicles are indexes 1 and 3.

You can read more about bitwise XOR operation here: <https://en.wikipedia.org/wiki/Bitwise_operation#XOR>.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.BigInteger;
import java.util.*;
 
 
public class Main{
	public static final int mod = 1000000007;
	
	public static void main(String[] args)throws IOException {
		// TODO Auto-generated method stub
		InputStream input = System.in;
		Reader in  = new Reader();
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
		int n = in.nextInt();
		int x = in.nextInt();
		int y = in.nextInt();
		
		
		String ss1 = null;
		String ss2 = null;
		int minc = n+1;
		int mini = -1;
		int diff[] = new int[11];
		for(int i=0; i<10; i++)
		{
			String s1 = "";
			String s2 = "";
			int c1 = 0;
			int c2 = 0;
			for(int j=1; j<n;j++)
			{
				if((j&(1<<i))== 0)
					{
						s1 += j+" ";
						c1++;
					}
				else
					{
						s2 += j+" ";
						c2++;
					}
				//System.out.println(s1);
				//System.out.println(s2);
			}
			if((n&(1<<i)) == 0)
				{
					s1 += n;
					c1++;
				}
			else 
				{
					s2 += n;
					c2++;
				}
			if(c1 > 0)
				System.out.println("? "+c1+" "+s1);
			else
				System.out.println("? "+c2+" "+s2);
			System.out.flush();
			int ans = in.nextInt();
			if(((c1 % 2 == 0 ) && (ans == (x^y)))||((c1 % 2 == 1) && (ans == y)))
			{	
				diff[i] = 1;
				if((c1 > 0 && minc > c1) || (c2 > 0 && minc > c2))
				{
					minc = Math.min(c1, c2);
					mini = i;
					diff[i] = 1;
				}
			}
			
		}
		
		ArrayList<Integer> a = new ArrayList<Integer>();
		ArrayList<Integer> b = new ArrayList<Integer>();
		for(int i=1; i<=n; i++)
		{
			if((i & (1<<mini)) != 0)
				a.add(i);
			else 
				b.add(i);
		}
		
		if(a.size() > b.size())
		{
			ArrayList<Integer> tmp = a;
			a = b;
			b = tmp;
		}
		int n1 = a.size();
		
		int aa[] = new int[n1];
				
		for(int i=0; i<n1; i++)
			aa[i] = a.get(i);
				
		
		int i1 = find(aa,n1,x,y);
		
		int i2 = i1;
		
		for(int i=0; i<=10; i++)
			if(diff[i] == 1)
			{
				
				i2 ^= (1<<i); 
			}
		
		if(i1 > i2)
		{
			int tmp = i1;
			i1 = i2;
			i2 = tmp;
		}
		
		System.out.println("! "+(i1)+" "+(i2));
		System.out.flush();
		
	}
	
	static int find(int a[],int n,int x,int y)throws IOException
	{
		Reader in  = new Reader();
		
		//System.out.println(Arrays.toString(a));
		//System.out.println(n);
		int l = 0;
		int r = n-1;
		
		while(l < r)
		{
			int mid = (l+r)/2;
			//System.out.println(l+" "+r+" "+mid);
			String op = "";
			for(int i=l; i<mid; i++)
			{
				op += a[i]+" ";
			}
			op += a[mid];
			System.out.println("? "+(1+mid-l)+" "+op);
			System.out.flush();
			int ans = in.nextInt();
			if(ans == (x^y) || ans == y)
			{
				r = mid;
				//System.out.println("**");
			}
			else
			{
				//System.out.println(l+" -");
				l = mid+1;
			}
		}
		
			return a[l];
	}
static int gcd(int a,int b)
{
	if(b == 0)
		return a;
	else return gcd(b,a%b);
}
static int lcm(int a, int b)
{
	
	return (a*b)/gcd(a,b);
}

	 static class Reader
	    {
	        final private int BUFFER_SIZE = 1 << 16;
	        private DataInputStream din;
	        private byte[] buffer;
	        private int bufferPointer, bytesRead;
	 
	        public Reader()
	        {
	            din = new DataInputStream(System.in);
	            buffer = new byte[BUFFER_SIZE];
	            bufferPointer = bytesRead = 0;
	        }
	 
	        public Reader(String file_name) throws IOException
	        {
	            din = new DataInputStream(new FileInputStream(file_name));
	            buffer = new byte[BUFFER_SIZE];
	            bufferPointer = bytesRead = 0;
	        }
	 
	        public String readLine() throws IOException
	        {
	            byte[] buf = new byte[64]; // line length
	            int cnt = 0, c;
	            while ((c = read()) != -1)
	            {
	                if (c == '\n')
	                    break;
	                buf[cnt++] = (byte) c;
	            }
	            return new String(buf, 0, cnt);
	        }
	 
	        public int nextInt() throws IOException
	        {
	            int ret = 0;
	            byte c = read();
	            while (c <= ' ')
	                c = read();
	            boolean neg = (c == '-');
	            if (neg)
	                c = read();
	            do
	            {
	                ret = ret * 10 + c - '0';
	            }  while ((c = read()) >= '0' && c <= '9');
	 
	            if (neg)
	                return -ret;
	            return ret;
	        }
	 
	        public long nextLong() throws IOException
	        {
	            long ret = 0;
	            byte c = read();
	            while (c <= ' ')
	                c = read();
	            boolean neg = (c == '-');
	            if (neg)
	                c = read();
	            do {
	                ret = ret * 10 + c - '0';
	            }
	            while ((c = read()) >= '0' && c <= '9');
	            if (neg)
	                return -ret;
	            return ret;
	        }
	 
	        public double nextDouble() throws IOException
	        {
	            double ret = 0, div = 1;
	            byte c = read();
	            while (c <= ' ')
	                c = read();
	            boolean neg = (c == '-');
	            if (neg)
	                c = read();
	 
	            do {
	                ret = ret * 10 + c - '0';
	            }
	            while ((c = read()) >= '0' && c <= '9');
	 
	            if (c == '.')
	            {
	                while ((c = read()) >= '0' && c <= '9')
	                {
	                    ret += (c - '0') / (div *= 10);
	                }
	            }
	 
	            if (neg)
	                return -ret;
	            return ret;
	        }
	 
	        private void fillBuffer() throws IOException
	        {
	            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
	            if (bytesRead == -1)
	                buffer[0] = -1;
	        }
	 
	        private byte read() throws IOException
	        {
	            if (bufferPointer == bytesRead)
	                fillBuffer();
	            return buffer[bufferPointer++];
	        }
	 
	        public void close() throws IOException
	        {
	            if (din == null)
	                return;
	            din.close();
	        }
	    }
}