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.
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.