FINDMAX - Finding Maximum

no tags 

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 seperated 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
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:0.131s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC PERL6 SQLITE VB.NET
Resource:own problem used for Codechef Snackdown Onsite