|
A |
Arrange
the Numbers |
Consider this sequence {1, 2, 3, … , N}, as a initial sequence of first
N natural numbers. You can rearrange this sequence in many ways. There
will be N! different arrangements. You have to calculate the number of
arrangement of first N natural numbers, where in first M (M<=N)
positions, exactly K (K<=M) numbers are in its initial position.
Example:
For, N = 5, M = 3, K =2
You should count this arrangement {1, 4, 3, 2, 5}, here in first 3
positions 1 is in 1st position and 3 in 3rd position. So
exactly 2 of its first 3 are in there initial position.
But you should not count this {1, 2, 3, 4, 5}.
Input
The first line of
input is an integer T(T<=1000) that indicates the number of test
cases. Next T line contains 3 integers each, N(1<=N<=1000), M,
and K.
Output
For each case,
output the case number, followed by the answer modulo 1000000007. Look
at the sample for clarification.
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1 |
Case |
Problem Setter :
Special Thanks : Abdullah Al Mahmud, Jane Alam Jan