Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict

def getlist():
	return list(map(int, input().split()))

const = 10 ** 9 + 7
MAX = 10 ** 5 + 50

#エラトステネス
L = [1 for i in range(100101)]
L[0] = 0
L[1] = 0
plist = []
for i in range(100101):
	if L[i] == 1:
		plist.append(i)
		c = 2
		while True:
			if i * c <= 100100:
				L[i * c] = 0
				c += 1
			else:
				break

#組み合わせ、逆元前計算
fac = [0] * (MAX)
inv = [0] * (MAX)
finv = [0] * (MAX)
fac[0], fac[1] = 1, 1
inv[1] = 1
finv[0], finv[1] = 1, 1

for i in range(2, MAX):
	fac[i] = fac[i - 1] * i % const
	inv[i] = inv[const % i] * (const - (const // i)) % const
	finv[i] = finv[i - 1] * inv[i] % const

#受け取り、処理
N, M = getlist()
if M == 1:
	print(1)
else:
	D = defaultdict(int)
	while M != 1:
		for i in plist:
			if M % i == 0:
				D[i] += 1
				M = M // i
				break

	data = []
	for i in D:
		data.append(D[i])

	#計算
	ans = 1
	for i in data:
		ans *= fac[i + N - 1] * finv[i] * finv[N - 1]
		ans %= const
	print(ans)

Fixed submission:
from collections import defaultdict

def getlist():
	return list(map(int, input().split()))

const = 10 ** 9 + 7
MAX = 10 ** 5 + 50

#エラトステネス
L = [1 for i in range(100001)]
L[0] = 0
L[1] = 0
plist = []
for i in range(100001):
	if L[i] == 1:
		plist.append(i)
		c = 2
		while True:
			if i * c <= 100000:
				L[i * c] = 0
				c += 1
			else:
				break

#組み合わせ、逆元前計算
fac = [0] * (MAX)
inv = [0] * (MAX)
finv = [0] * (MAX)
fac[0], fac[1] = 1, 1
inv[1] = 1
finv[0], finv[1] = 1, 1

for i in range(2, MAX):
	fac[i] = fac[i - 1] * i % const
	inv[i] = inv[const % i] * (const - (const // i)) % const
	finv[i] = finv[i - 1] * inv[i] % const

#受け取り、処理
N, M = getlist()
if M == 1:
	print(1)
else:
	D = defaultdict(int)
	while M != 1:
		judge = "No"
		for i in plist:
			if M % i == 0:
				D[i] += 1
				M = M // i
				judge = "Yes"
				break
		if judge == "No":
			D[M] += 1
			break

	data = []
	for i in D:
		data.append(D[i])

	#計算
	ans = 1
	for i in data:
		ans *= fac[i + N - 1] * finv[i] * finv[N - 1]
		ans %= const
	print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict

def getlist():
	return list(map(int, input().split()))

const = 10 ** 9 + 7
MAX = 10 ** 5 + 50

#エラトステネス
L = [1 for i in range(100001)]
L[0] = 0
L[1] = 0
plist = []
for i in range(100001):
	if L[i] == 1:
		plist.append(i)
		c = 2
		while True:
			if i * c <= 100000:
				L[i * c] = 0
				c += 1
			else:
				break

#組み合わせ、逆元前計算
fac = [0] * (MAX)
inv = [0] * (MAX)
finv = [0] * (MAX)
fac[0], fac[1] = 1, 1
inv[1] = 1
finv[0], finv[1] = 1, 1

for i in range(2, MAX):
	fac[i] = fac[i - 1] * i % const
	inv[i] = inv[const % i] * (const - (const // i)) % const
	finv[i] = finv[i - 1] * inv[i] % const

#受け取り、処理
N, M = getlist()
if M == 1:
	print(1)
else:
	D = defaultdict(int)
	while M != 1:
		for i in plist:
			if M % i == 0:
				D[i] += 1
				M = M // i
				break

	data = []
	for i in D:
		data.append(D[i])

	#計算
	ans = 1
	for i in data:
		ans *= fac[i + N - 1] * finv[i] * finv[N - 1]
		ans %= const
	print(ans)

Fixed submission:
from collections import defaultdict

def getlist():
	return list(map(int, input().split()))

const = 10 ** 9 + 7
MAX = 10 ** 5 + 50

#エラトステネス
L = [1 for i in range(100001)]
L[0] = 0
L[1] = 0
plist = []
for i in range(100001):
	if L[i] == 1:
		plist.append(i)
		c = 2
		while True:
			if i * c <= 100000:
				L[i * c] = 0
				c += 1
			else:
				break

#組み合わせ、逆元前計算
fac = [0] * (MAX)
inv = [0] * (MAX)
finv = [0] * (MAX)
fac[0], fac[1] = 1, 1
inv[1] = 1
finv[0], finv[1] = 1, 1

for i in range(2, MAX):
	fac[i] = fac[i - 1] * i % const
	inv[i] = inv[const % i] * (const - (const // i)) % const
	finv[i] = finv[i - 1] * inv[i] % const

#受け取り、処理
N, M = getlist()
if M == 1:
	print(1)
else:
	D = defaultdict(int)
	while M != 1:
		judge = "No"
		for i in plist:
			if M % i == 0:
				D[i] += 1
				M = M // i
				judge = "Yes"
				break
		if judge == "No":
			D[M] += 1
			break

	data = []
	for i in D:
		data.append(D[i])

	#計算
	ans = 1
	for i in data:
		ans *= fac[i + N - 1] * finv[i] * finv[N - 1]
		ans %= const
	print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict

def getlist():
	return list(map(int, input().split()))

const = 10 ** 9 + 7
MAX = 10 ** 5 + 50

#エラトステネス
L = [1 for i in range(100001)]
L[0] = 0
L[1] = 0
plist = []
for i in range(100001):
	if L[i] == 1:
		plist.append(i)
		c = 2
		while True:
			if i * c <= 100000:
				L[i * c] = 0
				c += 1
			else:
				break

#組み合わせ、逆元前計算
fac = [0] * (MAX)
inv = [0] * (MAX)
finv = [0] * (MAX)
fac[0], fac[1] = 1, 1
inv[1] = 1
finv[0], finv[1] = 1, 1

for i in range(2, MAX):
	fac[i] = fac[i - 1] * i % const
	inv[i] = inv[const % i] * (const - (const // i)) % const
	finv[i] = finv[i - 1] * inv[i] % const

#受け取り、処理
N, M = getlist()
if M == 1:
	print(1)
else:
	D = defaultdict(int)
	while M != 1:
		for i in plist:
			if M % i == 0:
				D[i] += 1
				M = M // i
				break

	data = []
	for i in D:
		data.append(D[i])

	#計算
	ans = 1
	for i in data:
		ans *= fac[i + N - 1] * finv[i] * finv[N - 1]
		ans %= const
	print(ans)

Fixed submission:
from collections import defaultdict

def getlist():
	return list(map(int, input().split()))

const = 10 ** 9 + 7
MAX = 10 ** 5 + 50

#エラトステネス
L = [1 for i in range(100001)]
L[0] = 0
L[1] = 0
plist = []
for i in range(100001):
	if L[i] == 1:
		plist.append(i)
		c = 2
		while True:
			if i * c <= 100000:
				L[i * c] = 0
				c += 1
			else:
				break

#組み合わせ、逆元前計算
fac = [0] * (MAX)
inv = [0] * (MAX)
finv = [0] * (MAX)
fac[0], fac[1] = 1, 1
inv[1] = 1
finv[0], finv[1] = 1, 1

for i in range(2, MAX):
	fac[i] = fac[i - 1] * i % const
	inv[i] = inv[const % i] * (const - (const // i)) % const
	finv[i] = finv[i - 1] * inv[i] % const

#受け取り、処理
N, M = getlist()
if M == 1:
	print(1)
else:
	D = defaultdict(int)
	while M != 1:
		judge = "No"
		for i in plist:
			if M % i == 0:
				D[i] += 1
				M = M // i
				judge = "Yes"
				break
		if judge == "No":
			D[M] += 1
			break

	data = []
	for i in D:
		data.append(D[i])

	#計算
	ans = 1
	for i in data:
		ans *= fac[i + N - 1] * finv[i] * finv[N - 1]
		ans %= const
	print(ans)