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
import java.io.*;
import java.math.*;
import java.util.*;

/**
 *
 * @author Saju
 *
 */

public class Main {

    private static int dx[] = { 1, 0, -1, 0 };
    private static int dy[] = { 0, -1, 0, 1 };

    private static final long INF = Long.MAX_VALUE;
    private static final int INT_INF = Integer.MAX_VALUE;
    private static final long NEG_INF = Long.MIN_VALUE;
    private static final int NEG_INT_INF = Integer.MIN_VALUE;
    private static final double EPSILON = 1e-10;

    private static final long MAX = (long) 1e12;
    
    private static final long MOD = 100000007;

    private static final int MAXN = 300005;
    private static final int MAXA = 1000007;
    private static final int MAXLOG = 22;
    private static final double PI = Math.acos(-1);
    
	public static void main(String[] args) throws IOException {

		InputReader in = new InputReader(System.in);
//		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

//         InputReader in = new InputReader(new FileInputStream("src/test.in"));
//         PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("src/test.out")));

		
		
/*



*/		
		
		int n = in.nextInt();
		int m = in.nextInt();
		Set<Integer> list = new HashSet<>();
		int[] cnt = new int[MAXA];
		int[] arr = new int[n];
		for(int i = 0; i < n; i++) {
			int a = in.nextInt();
			arr[i] = a;
			if(a <= m) {
				list.add(a);
				cnt[a]++;
			}
		}
		if(list.size() == 0) {
			out.println("1 0");
		}
		else {
			
			int l = 1;
			int kmax = 0;
			int[] cnt1 = new int[MAXA];
			for(int e : list) {
				int c = 1;
				while(true){
					if(c * e > m) {
						break;
					}
					cnt1[c * e] += cnt[e];
					c++;
				}
			}
			
			for(int i = 1; i <= m; i++) {
				if(cnt1[i] > kmax) {
					kmax = cnt1[i];
					l = i;
				}
			}
			out.println(l + " " + kmax);
			for(int i = 0; i < n; i++) {
				if(l % arr[i] == 0) {
					out.print((i + 1) + " ");
				}
			}
		}
		
		
		
		in.close();
		out.flush();
		out.close();
		System.exit(0);
	}

	private static List<Integer> getFactors(int m) {
		List<Integer> factors = new ArrayList<>();
		for(long i = 1; i * i <= m; i++) {
			if(m % i == 0) {
				int a = (int)i;
				int b = (int)(m / i);
				factors.add(a);
				if(a != b) {
					factors.add(b);
				}
			}
		}
		return factors;
	}

	private static class Pair{
		int x;
		int cnt;
		public Pair(int x, int cnt) {
			this.x = x;
			this.cnt = cnt;
		}
	}
	

	/*
	 * return the number of elements in list that are less than or equal to the val
	 */
	private static long upperBound(List<Long> list, long val) {
		int start = 0;
		int len = list.size();
		int end = len - 1;
		int mid = 0;

		while (true) {
			if (start > end) {
				break;
			}
			mid = (start + end) / 2;
			long v = list.get(mid);
			if (v == val) {
				start = mid;
				while(start < end) {
					mid = (start + end) / 2;
					if(list.get(mid) == val) {
						if(mid + 1 < len && list.get(mid + 1) == val) {
							start = mid + 1;
						}
						else {
							return mid + 1;
						}
					}
					else {
						end = mid - 1;
					}
				}
				return start + 1;
			}
			if (v > val) {
				end = mid - 1;
			} else {
				start = mid + 1;
			}
		}
		if (list.get(mid) < val) {
			return mid + 1;
		}
		return mid;
	}


	private static boolean isPalindrome(String str) {
		StringBuilder sb = new StringBuilder();
		sb.append(str);
		String str1 = sb.reverse().toString();
		return str.equals(str1);
	}

	private static String getBinaryStr(long n, int j) {
		String str = Long.toBinaryString(n);
		int k = str.length();
		for (int i = 1; i <= j - k; i++) {
			str = "0" + str;
		}

		return str;
	}
	
	private static long modInverse(long r) {
		return bigMod(r, MOD - 2, MOD);
	}
	
	private static long bigMod(long n, long k, long m) {

        long ans = 1;
        while (k > 0) {
            if ((k & 1) == 1) {
                ans = (ans * n) % m;
            }
            n = (n * n) % m;
            k >>= 1;
        }
        return ans;
    }
    
	private static long ceil(long n, long x) {
		long div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
	}
	
    private static int ceil(int n, int x) {
        int div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
    }

    
    private static int abs(int x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }
    
    private static double abs(double x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }

    private static long abs(long x) {
        if(x < 0) {
            return -x;
        }
        return x;
    }

    private static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }

    private static int gcd(int a, int b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }
    
    private static long gcd(long a, long b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    private static int log(long x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    private static long min(long a, long b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static int min(int a, int b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static long max(long a, long b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static int max(int a, int b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public String next() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());

                }
            } catch (IOException e) {
                return null;
            }
            return tokenizer.nextToken();
        }

        public String nextLine() {
            String line = null;
            try {
                tokenizer = null;
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

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

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

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

        public boolean hasNext() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());
                }
            } catch (Exception e) {
                return false;
            }
            return true;
        }
        
        public int[] nextIntArr(int n) {
        	int arr[] = new int[n];
    		for(int i = 0; i < n; i++) {
    			arr[i] = nextInt();
    		}
    		return arr;
        }
        
        public long[] nextLongArr(int n) {
        	long arr[] = new long[n];
    		for(int i = 0; i < n; i++) {
    			arr[i] = nextLong();
    		}
    		return arr;
        }
        
        public int[] nextIntArr1(int n) {
        	int arr[] = new int[n + 1];
    		for(int i = 1; i <= n; i++) {
    			arr[i] = nextInt();
    		}
    		return arr;
        }
        
        public long[] nextLongArr1(int n) {
        	long arr[] = new long[n + 1];
    		for(int i = 1; i <= n; i++) {
    			arr[i] = nextLong();
    		}
    		return arr;
        }
       
        public void close() {
        	try {
        		if(reader != null) {
        			reader.close();
        		}
        	}
        	catch(Exception e) {
        		
        	}
        	
        	
        }
    }

}