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A Tale of Two Queues

The two queues.
Following yet another all-nighter of studying patterns in permutations at the university, Unnar is both exhausted and starving. Fortunately it is almost noon, and the cafeteria has started serving lunch.

After heading downstairs, Unnar is sad to see that the cafeteria is already full of hungry students, and that the two queues towards the two registers are already quite long. Although he would prefer shorter queues, years of eating at the cafeteria has made Unnar an expert at estimating how long different individuals take to pay for their food at the register.

The methods Unnar uses to perform these very accurate estimations require years of training to even begin to understand, but they are based on observations such as whether the individual has their credit card or cash ready, the amount and cost of the items they intend to purchase, and whether they are staff members.

After making his complex estimations for each individual in each queue, Unnar would like to know which queue he should enter in order to get to the register as quickly as possible, assuming his estimations are correct (which they always are!). At this point his sleep deprivation is really starting to kick in, and he asks you to help him with this final task.

Input

The input consists of:

• One line with two integers $n$ and $m$ ($1 \le n,m \le 5\, 000$), the number of individuals in the left and right queues.

• One line with $n$ integers, the $i$th of which represents the estimated time, in seconds, for the $i$th individual in the left queue.

• One line with $m$ integers, the $i$th of which represents the estimated time, in seconds, for the $i$th individual in the right queue.

Individuals are listed in their queue order, with the next in queue being listed first.

Output

If it is quicker for Unnar to enter the left queue, output “left”. If it is quicker for Unnar to enter the right queue, output “right”. If it does not matter which queue Unnar enters, output “either”.

Sample Input 1 Sample Output 1
4 2
10 9 8 15
32 40

left

Sample Input 2 Sample Output 2
2 3
15 15
10 10 10

either

Sample Input 3 Sample Output 3
4 1
20 20 20 20
60

right

CPU Time limit 1 second
Memory limit 1024 MB