JOIN

 Problem Statement

Problem Statement for FindingFriend

### Problem Statement

Your friend just took part in a popular online programming contest. The participants were split across roomCount rooms, with each room containing exactly roomSize contestants. We will use n = roomCount * roomSize to denote the total number of contestants.

The contest was such that there were no ties. After the contest, each contestant had a distinct rank between 1 and n, inclusive. (The contestant with rank 1 is the winner.)

A room winner is the contestant with the best (i.e., smallest) rank in their room.

You do not know the final standings. The only thing you know are the ranks of all room winners. More precisely, you are given a int[] leaders with roomCount elements. The i-th element of leaders denotes the rank of the room winner of the i-th room.

Your friend just told you that her rank in this contest was friendPlace.

Return the number of different rooms in which your friend could have competed, given the information you have.

### Definition

 Class: FindingFriend Method: find Parameters: int, int[], int Returns: int Method signature: int find(int roomSize, int[] leaders, int friendPlace) (be sure your method is public)

### Notes

-The value of n is not explicitly given in the arguments, but can be computed as roomSize times the number of elements in leaders.

### Constraints

-roomSize will be between 1 and 1,000,000,000, inclusive.
-roomCount will be between 1 and 1,000, inclusive.
-Additionally, roomSize and roomCount will be such that n (that is, roomSize times roomCount) will not exceed 1,000,000,000.
-leaders will contain exactly roomCount elements.
-Each element of leaders will be between 1 and n, inclusive.
-All elements of leaders will be distinct.
-It is guaranteed there is at least one distribution of contestants into rooms that is consistent with leaders.
-friendPlace will be between 1 and n, inclusive.

### Examples

0)

 `2` `{5,1,2}` `4`
`Returns: 2`
 We have 6 contestants: 3 rooms with 2 contestants in each of them. Your friend finished 4-th. Given the information you have, there are only two possible distributions of contestant ranks into rooms: Room 1: ranks 5 and 6. Room 2: ranks 1 and 3. Room 3: ranks 2 and 4. Room 1: ranks 5 and 6. Room 2: ranks 1 and 4. Room 3: ranks 2 and 3. Your friend has competed either in room 2 or in room 3. There are two possible rooms, so the correct return value is 2.
1)

 `5` `{1,2,3,4,5}` `4`
`Returns: 1`
 You know for sure your friend is in room 4, as she is its room winner.
2)

 `6` `{10,5,1,4,2,20}` `9`
`Returns: 4`
 Your friend can be in either of the rooms 2, 3, 4, and 5.
3)

 `1000000000` `{1}` `700700700`
`Returns: 1`
4)

 `2` `{3,6,8,1,2}` `10`
`Returns: 5`

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2010, TopCoder, Inc. All rights reserved.

This problem was used for:
Single Round Match 700 Sponsored by Booz Allen Ham Round 1 - Division I, Level One