1735. Count Ways to Make Array With Product

N = 10020
MOD = 10**9 + 7
f = [1] * N
g = [1] * N
p = defaultdict(list)
for i in range(1, N):
    f[i] = f[i - 1] * i % MOD
    g[i] = pow(f[i], MOD - 2, MOD)
    x = i
    j = 2
    while j <= x // j:
        if x % j == 0:
            cnt = 0
            while x % j == 0:
                cnt += 1
                x //= j
            p[i].append(cnt)
        j += 1
    if x > 1:
        p[i].append(1)


def comb(n, k):
    return f[n] * g[k] * g[n - k] % MOD


class Solution:
    def waysToFillArray(self, queries: List[List[int]]) -> List[int]:
        res = []
        for n, k in queries:
            t = 1
            for x in p[k]:
                t = t * comb(x + n - 1, n - 1) % MOD
            res.append(t)
        return res