Vasya has been on vacation on Mars. He's a big fan of foreign coins, and thus has collected exactly one martian coin of each denomination, for a total of n coins: a₁ martian dollars, a₂ martian dollars, etc, a_n martian dollars. Unfortunately, he couldn't stand ordering the Pan Galactic Gargle Blaster at the Starport, and has to pay for it — it costs x martian dollars. Vasya is wondering which of his coins are absolutely necessary to do so (i.e., he is forced to abandon them). They don't offer change at the Starport Mars.

The input file contains two integer numbers n and x (1 ≤ n ≤ 200, 1 ≤ x ≤ 10⁴), followed by n distinct integer numbers a_i (1 ≤ a_i ≤ x).

On the first line of output, print the amount of denominations of coins that appear in any subset that sums to x martian dollars. On the second line of output, print the denominations themselves, in any order, separated with single spaces. It is guaranteed that there exists at least one way to pay x martian dollars with the given coins.

sample input	sample output
5 18 1 2 3 5 10	2 5 10