{"problem":{"name":"Factorization","description":{"content":"You are given positive integers $N$ and $M$. How many sequences $a$ of length $N$ consisting of positive integers satisfy $a_1 \\times a_2 \\times ... \\times a_N = M$? Find the count modulo $10^9+7$. He","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc110_d"},"statements":[{"statement_type":"Markdown","content":"You are given positive integers $N$ and $M$.\nHow many sequences $a$ of length $N$ consisting of positive integers satisfy $a_1 \\times a_2 \\times ... \\times a_N = M$? Find the count modulo $10^9+7$.\nHere, two sequences $a'$ and $a''$ are considered different when there exists some $i$ such that $a_i' \\neq a_i''$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq M \\leq 10^9$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc110_d","tags":[],"sample_group":[["2 6","4\n\nFour sequences satisfy the condition: ${a_1, a_2} = {1, 6}, {2, 3}, {3, 2}$ and ${6, 1}$."],["3 12","18"],["100000 1000000000","957870001"]],"created_at":"2026-03-03 11:01:14"}}