AtCoder Regular Contest 135
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Problem Statement
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You are given an integer $N$. On an integer sequence $A = (1, 2, \ldots, N)$, let us do the operation below exactly $K$ times.
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- Let
$n$be the current number of terms in$A$. For all$i$such that$1\leq i \leq n$and$i\equiv 1\pmod{3}$, delete the$i$-th term of$A$, simultaneously.
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Find the sum of the terms of $A$ after $K$ operations, modulo $998244353$.
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Constraints
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$1\leq N\leq 10^{14}$$1\leq K\leq 100$
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Input
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Input is given from Standard Input from the following format:
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N K翻译中…
Output
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Print the sum of the terms of $A$ after $K$ operations, modulo $998244353$.
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样例
Input #1
10 2
Output #1
25
- Initially, we have $A = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)$.
- After the first operation, we have $A = (2, 3, 5, 6, 8, 9)$.
- After the second operation, we have $A = (3, 5, 8, 9)$.
- The sum of the terms here is $3 + 5 + 8 + 9 = 25$.
Input #2
10 10
Output #2
0
- After the second operation, we have $A = (3, 5, 8, 9)$ (same as Sample Input 1).
- After the third operation, we have $A = (5, 8)$.
- After the fourth operation, we have $A = (8)$.
- After the fifth operation, $A$ is empty.
- In the sixth and subsequent operations, $A$ remains empty, where the sum of the terms is $0$.
Input #3
10000 10
Output #3
862816
题目信息
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