FINDMAX - Finding Maximum

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One way of finding the maximum element in an array is to initialize a variable to the first element in the array, iterate through the remaining array, and update the variable whenever a value strictly greater than it is found. Assuming that the array contains N elements each in the range 1..K, how many such arrays exist such that the above algorithm performs exactly P updates? Initialization of the variable is not counted as an update.

For example, the possible arrays for N = 4, K = 3 and P = 2 are:

  1. {1, 1, 2, 3}
  2. {1, 2, 1, 3}
  3. {1, 2, 2, 3}
  4. {1, 2, 3, 1}
  5. {1, 2, 3, 2}
  6. {1, 2, 3, 3}

Input

The first line contains T the number of test cases. There follow T lines, containing 3 space separated integers N, K and P.

Output

Output T lines, one for each test case. On each line, output the answer as asked above. Since the answers can get very big, output the answer modulo 1000000007.

Example

Sample Input:
3
4 3 2
2 3 1
3 4 1

Sample Output:
6
3
30

Constraints

1 <= T <= 100
1 <= n <= 100
1 <= K <= 300
0 <= P < n


hide comments
phantomhive: 2018-08-28 19:02:56

For this problem (p+1) <= k right?

Last edit: 2018-08-28 19:03:11
hello_world123: 2018-06-21 09:50:05

For those scratching their head , just think about finding the number of arrays of length n , and given k and p, assuming you already know the number of arrays of length <= n
for all possible values of k and p.

arpit_01: 2018-03-01 15:00:38

how to approach the recurrence relation?

nitesh kumar: 2014-06-18 12:05:08

optimization tips here:
precalculate the values
try avoid unnecessary iteration of loops [1..100][1..100][1..300] & use mod when needed & long long is sufficient..

:D: 2011-03-28 08:06:37

Not per test case, but per input :)

Pratham Khandelwal: 2011-01-28 12:25:30

Is O(n*K*P) per test case sufficient?
I am getting TLE


Added by:Varun Jalan
Date:2010-01-24
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
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