{"problem":{"name":"Product of Arithmetic Progression","description":{"content":"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 $1\\ 000\\ 003$. Y","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"m_solutions2019_e"},"statements":[{"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 $1\\ 000\\ 003$.\nYou are given $Q$ queries of this form. In the $i$\\-th query, compute the answer in case $x = x_i, d = d_i, n = n_i$.\n\n## Constraints\n\n*   $1 \\leq Q \\leq 10^5$\n*   $0 \\leq x_i, d_i \\leq 1\\ 000\\ 002$\n*   $1 \\leq n_i \\leq 10^9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$Q$\n$x_1$ $d_1$ $n_1$\n$:$\n$x_Q$ $d_Q$ $n_Q$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"m_solutions2019_e","tags":[],"sample_group":[["2\n7 2 4\n12345 67890 2019","9009\n916936\n\nFor the first query, the answer is $7 \\times 9 \\times 11 \\times 13 = 9009$. Don't forget to compute the answer modulo $1\\ 000\\ 003$."]],"created_at":"2026-03-03 11:01:14"}}