This is an interactive problem.

You are given two integers c and n. The jury has a randomly generated set A of distinct positive integers not greater than c (it is generated from all such possible sets with equal probability). The size of A is equal to n.

Your task is to guess the set A. In order to guess it, you can ask at most ⌈ 0.65 ⋅ c ⌉ queries.

In each query, you choose a single integer 1 ≤ x ≤ c. As the answer to this query you will be given the [bitwise xor sum](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all y, such that y ∈ A and gcd(x, y) = 1 (i.e. x and y are coprime). If there is no such y this xor sum is equal to 0.

You can ask all queries at the beginning and you will receive the answers to all your queries. After that, you won't have the possibility to ask queries.

You should find any set A', such that |A'| = n and A' and A have the same answers for all c possible queries.

Input

Firstly you are given two integers c and n (100 ≤ c ≤ 10^6, 0 ≤ n ≤ c).

Interaction

In the first line you should print an integer q (0 ≤ q ≤ ⌈ 0.65 ⋅ c ⌉) — the number of queries you want to ask. After that in the same line print q integers x_1, x_2, …, x_q (1 ≤ x_i ≤ c) — the queries.

For these queries you should read q integers, i-th of them is the answer to the described query for x = x_i.

After that you should print n distinct integers A'_1, A'_2, …, A'_n — the set A' you found.

If there are different sets A' that have the same answers for all possible queries, print any of them.

If you will ask more than ⌈ 0.65 ⋅ c ⌉ queries or if the queries will be invalid, the interactor will terminate immediately and your program will receive verdict Wrong Answer.

After printing the queries and answers do not forget to output end of line and flush the output buffer. Otherwise, you will get the Idleness limit exceeded verdict. To do flush use:

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



Hacks

You cannot make hacks in this problem.

Example

Input


10 6

1 4 2 11 4 4 4



Output


7 10 2 3 5 7 1 6

1 4 5 6 8 10

Note

The sample is made only for you to understand the interaction protocol. Your solution will not be tested on the sample.

In the sample A = \{1, 4, 5, 6, 8, 10\}. 7 queries are made, 7 ≤ ⌈ 0.65 ⋅ 10 ⌉ = 7, so the query limit is not exceeded.

Answers for the queries: 

  * For 10: 1 is the only number in the set A coprime with 10, so the answer is 1 
  * For 2: 1_{10} ⊕ 5_{10} = 001_2 ⊕ 101_2 = 4_{10}, where ⊕ is the bitwise xor 
  * For 3: 1_{10} ⊕ 4_{10} ⊕ 5_{10} ⊕ 8_{10} ⊕ 10_{10} = 0001_2 ⊕ 0100_2 ⊕ 0101_2 ⊕ 1000_2 ⊕ 1010_2 = 2_{10} 
  * For 5: 1_{10} ⊕ 4_{10} ⊕ 6_{10} ⊕ 8_{10} = 0001_2 ⊕ 0100_2 ⊕ 0110_2 ⊕ 1000_2 = 11_{10} 
  * For 7: 1_{10} ⊕ 4_{10} ⊕ 5_{10} ⊕ 6_{10} ⊕ 8_{10} ⊕ 10_{10} = 0001_2 ⊕ 0100_2 ⊕ 0101_2 ⊕ 0110_2 ⊕ 1000_2 ⊕ 1010_2 = 4_{10} 
  * For 1: 1_{10} ⊕ 4_{10} ⊕ 5_{10} ⊕ 6_{10} ⊕ 8_{10} ⊕ 10_{10} = 0001_2 ⊕ 0100_2 ⊕ 0101_2 ⊕ 0110_2 ⊕ 1000_2 ⊕ 1010_2 = 4_{10} 
  * For 6: 1_{10} ⊕ 5_{10} = 0001_2 ⊕ 0101_2 = 4_{10} 
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.System.arraycopy;
import static java.lang.System.exit;
import static java.util.Arrays.copyOf;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.BitSet;
import java.util.NoSuchElementException;
import java.util.Random;
import java.util.StringTokenizer;

public class H {

	static class IntList {

		int data[] = new int[3];
		int size = 0;

		boolean isEmpty() {
			return size == 0;
		}

		int size() {
			return size;
		}

		int get(int index) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			return data[index];
		}

		void clear() {
			size = 0;
		}

		void set(int index, int value) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			data[index] = value;
		}

		void expand() {
			if (size >= data.length) {
				data = copyOf(data, (data.length << 1) + 1);
			}
		}

		void insert(int index, int value) {
			if (index < 0 || index > size) {
				throw new IndexOutOfBoundsException();
			}
			expand();
			arraycopy(data, index, data, index + 1, size++ - index);
			data[index] = value;
		}

		int delete(int index) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			int value = data[index];
			arraycopy(data, index + 1, data, index, --size - index);
			return value;
		}

		void push(int value) {
			expand();
			data[size++] = value;
		}

		int pop() {
			if (size == 0) {
				throw new NoSuchElementException();
			}
			return data[--size];
		}

		void unshift(int value) {
			expand();
			arraycopy(data, 0, data, 1, size++);
			data[0] = value;
		}

		int shift() {
			if (size == 0) {
				throw new NoSuchElementException();
			}
			int value = data[0];
			arraycopy(data, 1, data, 0, --size);
			return value;
		}
	}

	static class LongList {

		long data[] = new long[3];
		int size = 0;

		boolean isEmpty() {
			return size == 0;
		}

		int size() {
			return size;
		}

		long get(int index) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			return data[index];
		}

		void clear() {
			size = 0;
		}

		void set(int index, long value) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			data[index] = value;
		}

		void expand() {
			if (size >= data.length) {
				data = copyOf(data, (data.length << 1) + 1);
			}
		}

		void insert(int index, long value) {
			if (index < 0 || index > size) {
				throw new IndexOutOfBoundsException();
			}
			expand();
			arraycopy(data, index, data, index + 1, size++ - index);
			data[index] = value;
		}

		long delete(int index) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			long value = data[index];
			arraycopy(data, index + 1, data, index, --size - index);
			return value;
		}

		void push(long value) {
			expand();
			data[size++] = value;
		}

		long pop() {
			if (size == 0) {
				throw new NoSuchElementException();
			}
			return data[--size];
		}

		void unshift(long value) {
			expand();
			arraycopy(data, 0, data, 1, size++);
			data[0] = value;
		}

		long shift() {
			if (size == 0) {
				throw new NoSuchElementException();
			}
			long value = data[0];
			arraycopy(data, 1, data, 0, --size);
			return value;
		}
	}

	static void sortBy(int a[], int n, int v[]) {
		if (n == 0) {
			return;
		}
		for (int i = 1; i < n; i++) {
			int j = i;
			int ca = a[i];
			int cv = v[ca];
			do {
				int nj = (j - 1) >> 1;
				int na = a[nj];
				if (cv <= v[na]) {
					break;
				}
				a[j] = na;
				j = nj;
			} while (j != 0);
			a[j] = ca;
		}
		int ca = a[0];
		for (int i = n - 1; i > 0; i--) {
			int j = 0;
			while ((j << 1) + 2 + Integer.MIN_VALUE < i + Integer.MIN_VALUE) {
				j <<= 1;
				j += (v[a[j + 2]] > v[a[j + 1]]) ? 2 : 1;
			}
			if ((j << 1) + 2 == i) {
				j = (j << 1) + 1;
			}
			int na = a[i];
			a[i] = ca;
			ca = na;
			int cv = v[ca];
			while (j != 0 && v[a[j]] < cv) {
				j = (j - 1) >> 1;
			}
			while (j != 0) {
				na = a[j];
				a[j] = ca;
				ca = na;
				j = (j - 1) >> 1;
			}
		}
		a[0] = ca;
	}

	static void solve() throws Exception {
		int c = scanInt(), n = scanInt();
		int lc[] = new int[c + 1];
		for (int i = 1; i * i <= c; i++) {
			for (int j = i; j * i <= c; j += i) {
				lc[j * i] = j;
			}
		}
		for (int i = 4; i <= c; i++) {
			lc[i] = lc[lc[i]];
		}
		int q = 0, x[] = new int[c];
		for (int i = 1; i <= c; i++) {
			if (lc[i] == i) {
				x[q++] = i;
			}
		}
		IntList cls[] = new IntList[q];
		for (int i = 0; i < q; i++) {
			cls[i] = new IntList();
		}
		int lcr[] = new int[c + 1];
		for (int i = 0; i < q; i++) {
			lcr[x[i]] = i;
		}
		for (int i = 1; i <= c; i++) {
			cls[lcr[lc[i]]].push(i);
		}
		out.print(q);
		for (int i = 0; i < q; i++) {
			out.print(' ');
			out.print(x[i]);
		}
		out.println();
		out.flush();
		int y[] = new int[c + 1];
		for (int i = 0; i < q; i++) {
			y[x[i]] = scanInt();
		}
		for (int i = c; i >= 1; i--) {
			if (lc[i] != i) {
				continue;
			}
			for (int j = i + i; j <= c; j += i) {
				if (lc[j] != j) {
					continue;
				}
				y[j] ^= y[i];
			}
		}
		for (int i = 1; i <= c; i++) {
			if (lc[i] != i) {
				continue;
			}
			for (int j = i + i; j <= c; j += i) {
				if (lc[j] != j) {
					continue;
				}
				y[i] ^= y[j];
			}
		}
		IntList ca = new IntList();
		LongList cb = new LongList();
		boolean ans[] = new boolean[c + 1];
		int ansN = 0;
		long lzeros[][] = new long[q][];
		BitSet bitZeros[][] = new BitSet[q][];
		int nZeros[] = new int[q];
		for (int i = 0; i < q; i++) {
			int cv = y[x[i]];
			IntList ccl = cls[i];
			int cn = ccl.size;
			if (cn < 64) {
				long cans = 0;
				ca.size = cb.size = cn;
				while (ca.data.length < cn) {
					ca.expand();
				}
				while (cb.data.length < cn) {
					cb.expand();
				}
				arraycopy(ccl.data, 0, ca.data, 0, cn);
				for (int j = 0; j < cn; j++) {
					cb.data[j] = 1L << j;
				}
				for (int bit = 19; bit >= 0; bit--) {
					int j;
					for (j = 0; j < cn; j++) {
						if ((ca.data[j] & (-1 << bit)) == 1 << bit) {
							break;
						}
					}
					if (j == cn) {
						if ((cv & (1 << bit)) != 0) {
							throw new AssertionError();
						}
						continue;
					}
					if ((cv & (1 << bit)) != 0) {
						cv ^= ca.data[j];
						cans ^= cb.data[j];
					}
					for (int jj = 0; jj < cn; jj++) {
						if (jj != j && (ca.data[jj] & (1 << bit)) != 0) {
							ca.data[jj] ^= ca.data[j];
							cb.data[jj] ^= cb.data[j];
						}
					}
				}
				for (int j = 0; j < cn; j++) {
					if ((cans & (1L << j)) != 0) {
						ans[ccl.data[j]] = true;
						++ansN;
					}
				}
				int nz = 0;
				for (int j = 0; j < cn; j++) {
					if (ca.data[j] == 0) {
						++nz;
					}
				}
				nZeros[i] = nz;
				lzeros[i] = new long[nz];
				nz = 0;
				for (int j = 0; j < cn; j++) {
					if (ca.data[j] == 0) {
						lzeros[i][nz++] = cb.data[j];
					}
				}
			} else {
				BitSet cans = new BitSet();
				ca.size = cn;
				while (ca.data.length < cn) {
					ca.expand();
				}
				arraycopy(ccl.data, 0, ca.data, 0, cn);
				BitSet ccb[] = new BitSet[cn];
				for (int j = 0; j < cn; j++) {
					ccb[j] = new BitSet();
					ccb[j].set(j);
				}
				for (int bit = 19; bit >= 0; bit--) {
					int j;
					for (j = 0; j < cn; j++) {
						if ((ca.data[j] & (-1 << bit)) == 1 << bit) {
							break;
						}
					}
					if (j == cn) {
						if ((cv & (1 << bit)) != 0) {
							throw new AssertionError();
						}
						continue;
					}
					if ((cv & (1 << bit)) != 0) {
						cv ^= ca.data[j];
						cans.xor(ccb[j]);
					}
					for (int jj = 0; jj < cn; jj++) {
						if (jj != j && (ca.data[jj] & (1 << bit)) != 0) {
							ca.data[jj] ^= ca.data[j];
							ccb[jj].xor(ccb[j]);
						}
					}
				}
				for (int j = 0; j < cn; j++) {
					if (cans.get(j)) {
						ans[ccl.data[j]] = true;
						++ansN;
					}
				}
				int nz = 0;
				for (int j = 0; j < cn; j++) {
					if (ca.data[j] == 0) {
						++nz;
					}
				}
				nZeros[i] = nz;
				bitZeros[i] = new BitSet[nz];
				nz = 0;
				for (int j = 0; j < cn; j++) {
					if (ca.data[j] == 0) {
						bitZeros[i][nz++] = ccb[j];
					}
				}
			}
		}
		int idx[] = new int[q];
		for (int i = 0; i < q; i++) {
			idx[i] = i;
		}
		sortBy(idx, q, nZeros);
		Random rng = new Random(42);
		while (ansN != n) {
			for (int i = q - 1; i >= 0; i--) {
				int ii = idx[i];
				if (nZeros[ii] == 0) {
					break;
				}
				IntList ccl = cls[ii];
				int cn = ccl.size;
				int j = rng.nextInt(nZeros[ii]);
				if (lzeros[ii] != null) {
					long z = lzeros[ii][j];
					for (int k = 0; k < cn; k++) {
						if ((z & (1L << k)) != 0) {
							ansN += (ans[ccl.data[k]] ^= true) ? 1 : -1;
						}
					}
				} else {
					BitSet z = bitZeros[ii][j];
					for (int k = 0; k < cn; k++) {
						if (z.get(k)) {
							ansN += (ans[ccl.data[k]] ^= true) ? 1 : -1;
						}
					}
				}
				if (ansN == n) {
					break;
				}
			}
		}
		for (int i = 1; i <= c; i++) {
			if (ans[i]) {
				out.print(i + " ");
			}
		}
	}

	static int scanInt() throws IOException {
		return parseInt(scanString());
	}

	static long scanLong() throws IOException {
		return parseLong(scanString());
	}

	static String scanString() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer tok;

	public static void main(String[] args) {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			solve();
			in.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			exit(1);
		}
	}
}