Divisors of Binomial Coefficient

AtCoder

IDabc227_g

Time2000ms

Memory256MB

Difficulty—

Find the number, modulo $998244353$, of positive divisors of a binomial coefficient $\displaystyle \binom{N}{K}$. ## Constraints * $1 \leq N \leq 10^{12}$ * $0 \leq K \leq \min(10^6,N)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

5 2

Output #1

4

We have $\displaystyle \binom{5}{2}=10$, which has four positive divisors: $1,2,5,10$.

Input #2

103 3

Output #2

8

We have $\displaystyle \binom{103}{3}=176851$, which has eight positive divisors.

Input #3

1000000000000 1000000

Output #3

110520107

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "Find the number, modulo $998244353$, of positive divisors of a binomial coefficient $\\displaystyle \\binom{N}{K}$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^{12}$\n*   $0 \\leq K \\leq \\min(10^6,N)$\n*   All ...",
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