An archery tournament is held according to the following rules. There are
- The two archers on each target compete with each other and determine a winner and a loser between them. Then all archers are rearranged as follows:
- The winners on targets
to inclusive move to the target on their left (i.e., targets to respectively). - The losers on targets
to inclusive, as well as the winner on target , remain on the same target. - The loser on target
moves to target .
- The winners on targets
The tournament continues for
You are the only archer to arrive for the tournament exactly on time. All other
All the
Knowing how skilled each of your competitors is, you want to insert yourself in such a way as to ensure that you will finish the tournament on a target with as small a number as possible. If there are multiple ways to do this, you prefer the one that starts at a target with as large a number as possible.
Write a program that, given the ranks of all archers, including yourself, as well as your competitors' arrangement on the line, determines on which target you should start the tournament, so that you can achieve your goals as defined above.
Constraints
Input Specification
Your program must read from standard input the following data:
The first line contains the integers
The next
The rest of these lines contain the ranks of the other archers, one archer per line, in the order in which they have arranged themselves (from left to right).
Each of these
Output Specification
Your program must write to standard output a single line containing a single integer between 1 and
Grading
For a number of tests, worth a total of 60 points,
Also, for some of these tests, worth a total of 20 points,
Sample Input 1
4 8
7
4
2
6
5
8
1
3
Sample Output 1
3
Explanation Of Sample 1
You are the second worst archer. If you start on target 1, you will then go to target 4 and stay there until the end. If you start on target 2 or 4, you will just stay there for the whole tournament. If you start on target 3, you will beat the worst archer and then move to target 2 and stay there.
Sample Input 2
4 9
2
1
5
8
3
4
7
6
Sample Output 2
2
Explanation Of Sample 2
You are the second best archer. The best one is already on target 1 and will stay there for the whole duration of the tournament. Thus, no matter where you start, you will always move from your target, going through all targets from 4 to 1 over and over again. In order for you to end on target 1 after 9 transitions, you have to start on target 2.
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