Time Limit: 2 sec / Memory Limit: 1024 MB
Score : 400 points
Problem Statement
There are KK blue balls and N−K red balls. The balls of the same color cannot be distinguished. Snuke and Takahashi are playing with these balls.
First, Snuke will arrange the N balls in a row from left to right.
Then, Takahashi will collect only the K blue balls. In one move, he can collect any number of consecutive blue balls. He will collect all the blue balls in the fewest moves possible.
How many ways are there for Snuke to arrange the N balls in a row so that Takahashi will need exactly i moves to collect all the blue balls? Compute this number modulo 109+7 for each ii such that 1≤i≤K
Constraints
- 1≤K≤N≤2000
Input
Input is given from Standard Input in the following format:
N K