use std::collections::HashMap; const MOD: usize = 1e9 as usize + 7; fn fact_inv(size: usize) -> (Vec, Vec) { let mut facts = vec![0usize; size+1]; let mut fact_invs = vec![0usize; size+1]; let mut invs = vec![0usize; size+1]; facts[0] = 1; facts[1] = 1; fact_invs[0] = 1; fact_invs[1] = 1; invs[1] = 1; for i in 2..=size { facts[i] = facts[i-1] * i % MOD; invs[i] = MOD - invs[MOD % i] * (MOD / i) % MOD; fact_invs[i] = fact_invs[i - 1] * invs[i] % MOD; } (facts, fact_invs) } fn comb(n: usize, r: usize, facts: &Vec, fact_invs: &Vec) -> usize { facts[n] * fact_invs[r] % MOD * fact_invs[n-r] % MOD } fn main() { let mut nk = String::new(); std::io::stdin().read_line(&mut nk).ok(); let nk: Vec = nk.trim().split_whitespace().map(|s| s.parse().unwrap()).collect(); let n = nk[0]; let k = nk[1]; let mut mapping = HashMap::new(); let mut target = n; for i in 2..=(n as f64).sqrt().floor() as usize { while target % i == 0 { *mapping.entry(i).or_insert(0usize) += 1; target /= i; } } if target > 1 { mapping.insert(n, 1); } let mut result = 1usize; let (_, fact_invs) = fact_inv(50); for &cnt in mapping.values() { let num = (1..=cnt).map(|i| (k+i)%MOD).fold(1usize, |x, y| x * y % MOD); result *= num * fact_invs[cnt] % MOD; result %= MOD; } println!("{}", result); }