Two scouting teams for a robotics league, Team A and Team B, have each ranked the same pool of eligible robot models by how eager they are to feature them in a joint showcase. Team A's ranking is a list of model codes ordered from most wanted (index 0) to least wanted; Team B's ranking is a separate list drawn from the same style of pool, also ordered from most wanted (index 0) to least wanted. A given model code may appear in one ranking, both rankings, or neither.

To pick the fairest joint showcase entrant, the organizers want the model code(s) that appear in BOTH rankings with the smallest possible sum of their two 0-indexed positions -- a low combined rank means both teams are eager to feature it early. If several model codes tie for the smallest sum, all of them must be reported.

It is guaranteed the two rankings share at least one model code in common.

Input format

Line 1: two integers n and m -- the number of model codes in Team A's ranking and in Team B's ranking, respectively. Line 2: n space-separated model codes, Team A's ranking from index 0 (most wanted) to index n-1 (least wanted). Line 3: m space-separated model codes, Team B's ranking from index 0 (most wanted) to index m-1 (least wanted).

Output format

Print every model code that attains the minimum combined rank sum, one per line, in the order each code appears in Team A's ranking (index 0 first). Print nothing else.

Constraints

• 1 <= n, m <= 1000
• Each model code consists of 1 to 30 lowercase English letters and/or digits.
• No model code repeats within a single team's ranking.
• The two rankings share at least one model code.

3 3
falcon viper cobra
cobra falcon viper

falcon

2 2
shadow raptor
raptor shadow

shadow
raptor