Buggy python submission (verdict: Time Limit Exceeded):
import math

N, M = map(int, input().split())
max = int(math.sqrt(M))
mod = 7 + 10**9
F = []

def Prime(i): #素数であればTrueを返す
    root = math.sqrt(i)
    j, div = 2, False
    while j <= root:
        if i % j == 0:
            div = True
            break
        j += 1
    return (True if not div else False)

def comb(n, r):
    ans = math.factorial(n) // (math.factorial(n-r) * math.factorial(r))
    return ans % mod


ans = 1
for i in range(2, max + 1):
    if M % i == 0:
        div = M // i
        if Prime(i):
            pow = 0
            while M % (i ** (pow+1)) == 0:
                pow += 1
            ans *= comb(pow + N -1, pow)
            ans %= mod
        if Prime(div):
            pow = 0
            while M % (i ** (pow+1)) == 0:
                pow += 1
            ans *= comb(pow + N - 1, pow)
            ans %= mod

print(ans)

Fixed submission:
import math

def InvMod(i, pow, mod): #階乗のmodを計算
    if pow == 1:
        return i % mod
    else:
        if pow % 2 == 0:
            return InvMod((i**2) % mod, pow//2, mod) % mod
        else:
            return InvMod((i**2) % mod, pow//2, mod) * i % mod

def Prime(i): #素数であればTrueを返す
    root = math.sqrt(i)
    j, div = 2, True
    while j <= root:
        if i % j == 0:
            div = False
            break
        j += 1
    return div

N, M = map(int, input().split())
max = int(math.sqrt(M))
mod = 7 + 10**9

Pinv = [0]
Pfact = 1
for i in range(1, 31): #(階乗)^-1の計算, 2^31 > 10^9なので階乗は高々30乗まで
    Pfact *= i
    Pfact %= mod
    Pinv.append(InvMod(Pfact, mod-2, mod))

P = []
for i in range(2, max+1): #素因数の列挙
    if M % i == 0:
        if Prime(i):
            P.append(i)
        if Prime(M//i) and i**2 != M:
            P.append(M//i)

ans = 1
for p in P:
    C, pow = M, 0
    while C % p == 0: 
        pow += 1
        C //= p
    comb = Pinv[pow]  #(N-1)!/pow!(N-1)!
    for i in range(pow): #comb * (N-1+1)(N-1+2)…(N-1+pow)
        comb *= (N+i)
        comb %= mod
    ans *= comb
    ans %= mod

print(ans)

Buggy python submission (verdict: Runtime Error):
import math
N, M = map(int, input().split())
max = int(math.sqrt(M))
mod = 7 + 10**9
F = []
for i in range(1, max+1):
    if M%i == 0:
        F.append(i)
        F.append(M//i)

def DP(i, n, memo = {}): 
    if i == 1 or n==1:
        return 1
    try:
        return memo[(i, n)]
    except KeyError:
        ans = 0
        for j in F:
            if n//j >= 1 and n%j == 0:
                ans += DP(i-1, n//j, memo)
                ans %= mod
        memo[(i, n)] = ans
        return ans

memo = {}
print(DP(N, M, memo))

Fixed submission:
import math

def InvMod(i, pow, mod): #階乗のmodを計算
    if pow == 1:
        return i % mod
    else:
        if pow % 2 == 0:
            return InvMod((i**2) % mod, pow//2, mod) % mod
        else:
            return InvMod((i**2) % mod, pow//2, mod) * i % mod

def Prime(i): #素数であればTrueを返す
    root = math.sqrt(i)
    j, div = 2, True
    while j <= root:
        if i % j == 0:
            div = False
            break
        j += 1
    return div

N, M = map(int, input().split())
max = int(math.sqrt(M))
mod = 7 + 10**9

Pinv = [0]
Pfact = 1
for i in range(1, 31): #(階乗)^-1の計算, 2^31 > 10^9なので階乗は高々30乗まで
    Pfact *= i
    Pfact %= mod
    Pinv.append(InvMod(Pfact, mod-2, mod))

P = []
for i in range(2, max+1): #素因数の列挙
    if M % i == 0:
        if Prime(i):
            P.append(i)
        if Prime(M//i) and i**2 != M:
            P.append(M//i)

ans = 1
for p in P:
    C, pow = M, 0
    while C % p == 0: 
        pow += 1
        C //= p
    comb = Pinv[pow]  #(N-1)!/pow!(N-1)!
    for i in range(pow): #comb * (N-1+1)(N-1+2)…(N-1+pow)
        comb *= (N+i)
        comb %= mod
    ans *= comb
    ans %= mod

print(ans)