{"raw_statement":[{"iden":"problem statement","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 $a_i' \\neq a_i''$."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq M \\leq 10^9$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"2 6"},{"iden":"sample output 1","content":"4\n\nFour sequences satisfy the condition: ${a_1, a_2} = {1, 6}, {2, 3}, {3, 2}$ and ${6, 1}$."},{"iden":"sample input 2","content":"3 12"},{"iden":"sample output 2","content":"18"},{"iden":"sample input 3","content":"100000 1000000000"},{"iden":"sample output 3","content":"957870001"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}