Product of numbers

Input

First line contains two integers $n$ and $m$ ($1$ $\le$ $n$ $\le$ $100$, $1$ $\le$ $m$ $\le$ $10000$). Second line contains $n$ integers A_1, A_2, $\dots$, A_n ($0$ $\le$ A_i $\le$ $10000$).

Output

Print in the first line numbers $p$ and $k$ - the product of chosen numbers by modulo $m$ and the number of chosen numbers. Print in the second line $k$ numbers B_1, B_2, $\dots$, B_k - the indexes of chosen numbers. The indexes must be pairwise different. If there are multiple answers with maximum $p$, print any of them.

Examples