{"raw_statement":[{"iden":"problem statement","content":"Find the number, modulo $998244353$, of positive divisors of a binomial coefficient $\\displaystyle \\binom{N}{K}$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^{12}$\n*   $0 \\leq K \\leq \\min(10^6,N)$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$"},{"iden":"sample input 1","content":"5 2"},{"iden":"sample output 1","content":"4\n\nWe have $\\displaystyle \\binom{5}{2}=10$, which has four positive divisors: $1,2,5,10$."},{"iden":"sample input 2","content":"103 3"},{"iden":"sample output 2","content":"8\n\nWe have $\\displaystyle \\binom{103}{3}=176851$, which has eight positive divisors."},{"iden":"sample input 3","content":"1000000000000 1000000"},{"iden":"sample output 3","content":"110520107"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}