CodeForces 632D Longest Subsequence（数论）

题意：求一个最长子序列使得序列中的数的lcm小于m

思路：lcm与数的顺序没有关系，所以我们记录每个数出现的次数，然后类似筛法一样去找每一个数的因子有多少个就好了

#include<bits/stdc++.h>using namespace std;const int maxn = 1e6+5;int cnt[maxn];int dp[maxn];int a[maxn];int main(){    int n,m;    scanf("%d%d",&n,&m);    for(int i=1;i<=n;i++)    {        scanf("%d",&a[i]);        if(a[i]<=m)cnt[a[i]]++;    }    for(int i=m;i;i--)        for(int j=i;j<=m;j+=i)            dp[j]+=cnt[i];    long long ans1=-1,ans2=-1;    for(int i=1;i<=m;i++)        if(dp[i]>ans1)            ans1=dp[i],ans2=i;    cout<<ans2<<" "<<ans1<<endl;    for(int i=1;i<=n;i++)        if(ans2%a[i]==0)            cout<<i<<" ";    cout<<endl;}

Description

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 a_i (1 ≤ a_i ≤ 10⁹) — the elements of a.

Output

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

In the second line print k_max 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.

Sample Input

Input

7 86 2 9 2 7 2 3

Output

6 51 2 4 6 7

Input

6 42 2 2 3 3 3

Output

2 31 2 3