Product of Arithmetic Progression

AtCoder

IDm_solutions2019_e

Time2000ms

Memory256MB

Difficulty—

Consider the following arithmetic progression with $n$ terms: * $x, x + d, x + 2d, \ldots, x + (n-1)d$ What is the product of all terms in this sequence? Compute the answer modulo $1\ 000\ 003$. You are given $Q$ queries of this form. In the $i$\-th query, compute the answer in case $x = x_i, d = d_i, n = n_i$. ## Constraints * $1 \leq Q \leq 10^5$ * $0 \leq x_i, d_i \leq 1\ 000\ 002$ * $1 \leq n_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $Q$ $x_1$ $d_1$ $n_1$ $:$ $x_Q$ $d_Q$ $n_Q$ [samples]

Samples

Input #1

2
7 2 4
12345 67890 2019

Output #1

9009
916936

For the first query, the answer is $7 \times 9 \times 11 \times 13 = 9009$. Don't forget to compute the answer modulo $1\ 000\ 003$.

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "Consider the following arithmetic progression with $n$ terms:\n\n*   $x, x + d, x + 2d, \\ldots, x + (n-1)d$\n\nWhat is the product of all terms in this sequence? Compute the answer modulo $1\\ 000\\ 003$.\nY...",
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