Buggy python submission (verdict: Runtime Error):
# D - Factorization

N, M = map(int, input().split())
MOD = 10**9 + 7

def prime_factorization(n):
    prime_factors = []
    if n < 2:
        return 0
    for i in range(2, int(pow(n, 0.5)+1)):
        if n%i==0:
            ex = 0
            while n%i==0:
                ex += 1
                n //= i
            prime_factors.append((i, ex))
    if n!=1:
        prime_factors.append((n,1))
    return prime_factors

fac = [1, 1]
inv = [0, 1]
finv = [1, 1]

for i in range(2, N+36):
    fac.append(fac[-1] * i % MOD)
    inv.append(MOD - inv[MOD%i] * (MOD//i) % MOD)
    finv.append(finv[-1] * inv[-1] % MOD)

def comb_mod(n, r, m):
    if (n<0 or r<0 or n<r): return 0
    r = min(r, n-r)
    return fac[n] * finv[n-r] * finv[r] % m

primes = prime_factorization(M)
ans = 1
for p, ex in primes:
    ans = (ans * comb_mod(ex+N-1, N-1, MOD)) % MOD

print(ans)

Fixed submission:
# D - Factorization

N, M = map(int, input().split())
MOD = 10**9 + 7

def prime_factorization(n):
    prime_factors = []
    if n < 2:
        return 0
    for i in range(2, int(pow(n, 0.5)+1)):
        if n%i==0:
            ex = 0
            while n%i==0:
                ex += 1
                n //= i
            prime_factors.append((i, ex))
    if n!=1:
        prime_factors.append((n,1))
    return prime_factors

fac = [1, 1]
inv = [0, 1]
finv = [1, 1]

for i in range(2, N+36):
    fac.append(fac[-1] * i % MOD)
    inv.append(MOD - inv[MOD%i] * (MOD//i) % MOD)
    finv.append(finv[-1] * inv[-1] % MOD)

def comb_mod(n, r, m):
    if (n<0 or r<0 or n<r): return 0
    r = min(r, n-r)
    return fac[n] * finv[n-r] * finv[r] % m

primes = prime_factorization(M)
ans = 1
if primes != 0:
    for (p, ex) in primes:
        ans = (ans * comb_mod(ex+N-1, N-1, MOD)) % MOD

print(ans)

Buggy python submission (verdict: Runtime Error):
# D - Factorization

N, M = map(int, input().split())
MOD = 10**9 + 7

# M を素因数分解する 12 -> 2^2 * 3^1
# 2^2 と 3^1 の組み合わせをそれぞれ計算する。
# 2^2 は べき数を配分する組み合わせ。
# N=3の時、
# 2^2, 2^0, 2^0 -> 4, 1, 1
# 2^1, 2^1, 2^0 -> 2, 2, 1
# この組み合わせは べき数をxとした時、
# N-1個の区切り場所を追加したと仮定して、
# (x+N-1)C(N-1) 

def prime_factorization(n):
    prime_factors = []
    if n < 2:
        return 0
    for i in range(2, int(pow(n, 0.5)+1)):
        if n%i==0:
            ex = 0
            while n%i==0:
                ex += 1
                n //= i
            prime_factors.append((i, ex))
    # 割り切れなかった残りのnが1でない(素数)場合、リストに加える
    if n!=1:
        prime_factors.append((n,1))
    return prime_factors

fac = [1, 1]
inv = [0, 1]
finv = [1, 1]

for i in range(2, N+30):
    fac.append(fac[-1] * i % MOD)
    inv.append(MOD - inv[MOD%i] * (MOD//i) % MOD)
    finv.append(finv[-1] * inv[-1] % MOD)

def comb_mod(n, r, m):
    if (n<0 or r<0 or n<r): return 0
    r = min(r, n-r)
    return fac[n] * finv[n-r] * finv[r] % m

primes = prime_factorization(M)
ans = 1
for p, ex in primes:
    ans = (ans * comb_mod(ex+N-1, N-1, MOD)) % MOD

print(ans)

Fixed submission:
# D - Factorization

N, M = map(int, input().split())
MOD = 10**9 + 7

def prime_factorization(n):
    prime_factors = []
    if n < 2:
        return 0
    for i in range(2, int(pow(n, 0.5)+1)):
        if n%i==0:
            ex = 0
            while n%i==0:
                ex += 1
                n //= i
            prime_factors.append((i, ex))
    if n!=1:
        prime_factors.append((n,1))
    return prime_factors

fac = [1, 1]
inv = [0, 1]
finv = [1, 1]

for i in range(2, N+36):
    fac.append(fac[-1] * i % MOD)
    inv.append(MOD - inv[MOD%i] * (MOD//i) % MOD)
    finv.append(finv[-1] * inv[-1] % MOD)

def comb_mod(n, r, m):
    if (n<0 or r<0 or n<r): return 0
    r = min(r, n-r)
    return fac[n] * finv[n-r] * finv[r] % m

primes = prime_factorization(M)
ans = 1
if primes != 0:
    for (p, ex) in primes:
        ans = (ans * comb_mod(ex+N-1, N-1, MOD)) % MOD

print(ans)