Buggy python submission (verdict: Time Limit Exceeded):
import sys
from collections import defaultdict
def input(): return sys.stdin.readline().strip()
mod = 10**9+7

class Combination:
    """
    O(n)の前計算を1回行うことで，O(1)でnCr mod mを求められる
    n_max = 10**6のとき前処理は約950ms (PyPyなら約340ms, 10**7で約1800ms)
    使用例：
    comb = Combination(1000000)
    print(comb(5, 3))  # 10
    """
    def __init__(self, n_max, mod=10**9+7):
        self.mod = mod
        self.modinv = self.make_modinv_list(n_max)
        self.fac, self.facinv = self.make_factorial_list(n_max)

    def __call__(self, n, r):
        return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod

    def make_factorial_list(self, n):
        # 階乗のリストと階乗のmod逆元のリストを返す O(n)
        # self.make_modinv_list()が先に実行されている必要がある
        fac = [1]
        facinv = [1]
        for i in range(1, n+1):
            fac.append(fac[i-1] * i % self.mod)
            facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
        return fac, facinv

    def make_modinv_list(self, n):
        # 0からnまでのmod逆元のリストを返す O(n)
        modinv = [0] * (n+1)
        modinv[1] = 1
        for i in range(2, n+1):
            modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
        return modinv

def get_sieve_of_eratosthenes(n):
    """
    エラトステネスの篩
    """
    if not isinstance(n, int):
        raise TypeError('n is int type.')
    if n < 2:
        return []
    prime = [2]
    limit = int(n**0.5)
    data = [i + 1 for i in range(2, n, 2)]
    while True:
        p = data[0]
        if limit < p:
            return prime + data
        prime.append(p)
        data = [e for e in data if e % p != 0]
    return data

def main():
    comb = Combination(5 * 10**5)
    N, M = map(int, input().split())
    primes = get_sieve_of_eratosthenes(M)
    cand = []
    for p in primes:
        num = 0
        while M % p == 0:
            M //= p
            num += 1
        if num > 0: cand.append(num)

    ans = 1
    for num in cand:
        ans *= comb(num + (N - 1), num)
        ans %= mod
    print(ans)





if __name__ == "__main__":
    main()


Fixed submission:
import sys, math
from collections import defaultdict
def input(): return sys.stdin.readline().strip()
mod = 10**9+7

class Combination:
    def __init__(self, n_max, mod=10**9+7):
        self.mod = mod
        self.modinv = self.make_modinv_list(n_max)
        self.fac, self.facinv = self.make_factorial_list(n_max)

    def __call__(self, n, r):
        return self.fac[n] * self.facinv[r] % self.mod * self.facinv[n-r] % self.mod

    def make_factorial_list(self, n):
        fac = [1]
        facinv = [1]
        for i in range(1, n+1):
            fac.append(fac[i-1] * i % self.mod)
            facinv.append(facinv[i-1] * self.modinv[i] % self.mod)
        return fac, facinv

    def make_modinv_list(self, n):
        modinv = [0] * (n+1)
        modinv[1] = 1
        for i in range(2, n+1):
            modinv[i] = self.mod - self.mod//i * modinv[self.mod%i] % self.mod
        return modinv

def factorization(n):
    if n == 1: print("n must be > 1")
    arr = []
    temp = n
    for i in range(2, int(round(n ** 0.5))+1):
        cnt = 0
        while temp % i == 0:
            cnt += 1
            temp //= i
        if cnt > 0: arr.append([i, cnt])
    if temp != 1: arr.append([temp, 1])
    if arr == []: arr.append([n, 1])
    return arr


def main():
    comb = Combination(10**6)
    N, M = map(int, input().split())
    if M == 1:
        print(1)
        return
        
    primes = factorization(M)
    ans = 1
    for _, num in primes:
        ans *= comb(num + (N - 1), num)
        ans %= mod
    print(ans)





if __name__ == "__main__":
    main()