AtCoder Grand Contest 068
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Problem Statement
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There is a circle with circumference $L$, and $L$ people are standing equally spaced along the circumference. They are labeled as person $0, 1, \cdots, L-1$ in clockwise order. Consider choosing $N$ from these $L$ people. The cost of a choice is defined as follows.
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- For every pair of persons among the
$N$chosen people, find the minimum distance one person has to move along the circumference to reach the other person's position. The maximum value among these distances is the cost.
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Find the sum of costs over all possible choices, modulo $998244353$.
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Constraints
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$2 \leq N \leq L \leq 10^6$- All input values are integers.
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Input
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The input is given from Standard Input in the following format:
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L N翻译中…
Output
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Print the answer.
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样例
Input #1
4 2
Output #1
8
The choices of $N$ people and their corresponding costs are as follows:
- $(0,1)$: cost $1$
- $(0,2)$: cost $2$
- $(0,3)$: cost $1$
- $(1,2)$: cost $1$
- $(1,3)$: cost $2$
- $(2,3)$: cost $1$
The sum of these costs, $8$, is the answer.
Input #2
5 5
Output #2
2
We can only choose all of them. In this case, the cost is $2$.
Input #3
13 5
Output #3
7618
Input #4
1000000 100000
Output #4
664396470
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。