AtCoder Beginner Contest 205
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Problem Statement
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How many ways are there to arrange $N$ white balls and $M$ black balls in a row from left to right to satisfy the following condition?
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- For each
$i$$(1 \leq i \leq N + M)$, let$w_i$and$b_i$be the number of white balls and black balls among the leftmost$i$balls, respectively. Then,$w_i \leq b_i + K$holds for every$i$.
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Since the count can be enormous, find it modulo $(10^9 + 7)$.
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Constraints
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$0 \leq N, M \leq 10^6$$1 \leq N + M$$0 \leq K \leq N$- All values in input are integers.
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Input
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Input is given from Standard Input in the following format:
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N M K翻译中…
Output
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Print the answer. Be sure to find the count modulo $(10^9 + 7)$.
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样例
Input #1
2 3 1
Output #1
9
There are $10$ ways to arrange $2$ white balls and $3$ black balls in a row, as shown below, where `w` and `b` stand for a white ball and a black ball, respectively.
`wwbbb` `wbwbb` `wbbwb` `wbbbw` `bwwbb` `bwbwb` `bwbbw` `bbwwb` `bbwbw` `bbbww`
Among them, `wwbbb` is the only one that does not satisfy the condition. Here, there are $2$ white balls and $0$ black balls among the $2$ leftmost balls, and we have $2 > 0 + K = 1$.
Input #2
1 0 0
Output #2
0
There may be no way to satisfy the condition.
Input #3
1000000 1000000 1000000
Output #3
192151600
Be sure to print the count modulo $(10^9 + 7)$.
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。