You are given array a with n elements and the number m. Consider some subsequence of a and the value of least common multiple (LCM) of its elements. Denote LCM as l. Find any longest subsequence of a with the value l ≤ m.

A subsequence of a is an array we can get by erasing some elements of a. It is allowed to erase zero or all elements.

The LCM of an empty array equals 1.

Input

The first line contains two integers n and m (1 ≤ n, m ≤ 106) — the size of the array a and the parameter from the problem statement.

The second line contains n integers ai (1 ≤ ai ≤ 109) — the elements of a.

Output

In the first line print two integers l and kmax (1 ≤ l ≤ m, 0 ≤ kmax ≤ n) — the value of LCM and the number of elements in optimal subsequence.

In the second line print kmax integers — the positions of the elements from the optimal subsequence in the ascending order.

Note that you can find and print any subsequence with the maximum length.

Examples

Input

7 8
6 2 9 2 7 2 3


Output

6 5
1 2 4 6 7


Input

6 4
2 2 2 3 3 3


Output

2 3
1 2 3
/**
 * Created by Aminul on 11/28/2018.
 */

import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class CF632D {
    public static void main(String[] args)throws Exception {
        FastReader in = new FastReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt(), m = in.nextInt();
        int f[] = new int[m+1];
        List<Integer> g[] = genList(m+1);
        for (int i = 1; i <= n; i++) {
            int x = in.nextInt();
            if(x > m) continue;
            f[x]++;
            g[x].add(i);
        }

        int len[] = new int[m+1];
        int maxLen = 0, lcm = 1;
        for (int i = 1; i <= m; i++) {
            for(int j = i; j <= m; j += i) {
                len[j] += f[i];
                if(len[j] > maxLen) {
                    maxLen = len[j];
                    lcm = j;
                }
            }
        }

        List<Integer> res = new ArrayList<>();
        for(int i = 1; i <= m; i++) {
            if(lcm % i == 0) res.addAll(g[i]);
        }
        Collections.sort(res);
        pw.println(lcm+" "+res.size());
        for(int i : res) pw.print(i+" " );
        pw.println();
        pw.close();
    }

    static long gcd(long p, long q) {
        if (q == 0) return p;
        else return gcd(q, p % q);
    }

    static long lcm(long p, long q) {
        long g = gcd(p, q);
        p /= g;
        return p*q;
    }

    static <T>List<T>[] genList(int n){
        List<T> list[] = new List[n];
        for(int i = 0; i < n; i++) list[i] = new ArrayList<T>();
        return list;
    }

    static void debug(Object...obj) {
        System.err.println(Arrays.deepToString(obj));
    }

    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;

        public FastReader(InputStream is) {
            this.is = is;
        }

        public int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        public String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }



        public String nextLine() {
            int c = skip();
            StringBuilder sb = new StringBuilder();
            while (!isEndOfLine(c)){
                sb.appendCodePoint(c);
                c = readByte();
            }
            return sb.toString();
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

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

        public char[] next(int n) {
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        public char readChar() {
            return (char) skip();
        }
    }
}