Buggy python submission (verdict: Time Limit Exceeded):
n,m = map(int,input().split())
INF = 10**9+7
inv = {}
inv[0] = 1
inv[1] = 1
def p(x):
    if x in inv:
        return inv[x]
    else:
        inv[x] = ((-1)* p(INF%x) * (INF//x))% INF
        return inv[x]
# n H y
memo = [0 for i in range(m+1)]
def f(y):
    def g(v):
        if v == 0:
            return 1
        elif v == 1:
            return n
        elif memo[v] != 0:
            return memo[v]
        else:
            memo[v] = ((n+v-1)*g(v-1)*p(v))%INF
            return memo[v]
    return g(y)
# M を素因数分解
def h(x):
    t = x
    d = {}
    for i in range(2,x):
        if i*i > x:
            break
        if t % i != 0:
            continue
        if t % i == 0:
            ind = 0
            while t % i == 0:
                t = t // i
                ind += 1
            d[i] = ind
    if t != 1:
        d[x] = 1
    return d

res = 1
for i in h(m):
    res = (res *  f(h(m)[i])) % INF

print(res)

Fixed submission:
n,m = map(int,input().split())
INF = 10**9+7
inv = {}
inv[0] = 1
inv[1] = 1
def p(x):
    if x in inv:
        return inv[x]
    else:
        inv[x] = ((-1)* p(INF%x) * (INF//x))% INF
        return inv[x]
# n H i
l = [1] * 31
l[1] = n 
for i in range(2,31):
    l[i] = ((n+i-1)*l[i-1]*p(i))%INF
# M を素因数分解
def h(x):
    t = x
    d = {}
    for i in range(2,x):
        if i*i > x:
            break
        if t % i != 0:
            continue
        if t % i == 0:
            ind = 0
            while t % i == 0:
                t = t // i
                ind += 1
            d[i] = ind
    if t != 1:
        d[x] = 1
    return d

res = 1
for i in h(m):
    res = (res *  l[h(m)[i]]) % INF

print(res)

Buggy python submission (verdict: Time Limit Exceeded):
n,m = map(int,input().split())
INF = 10**9+7
# x個の区別できる箱にy個の区別できない球を入れる場合の数
memo = [[0 for i in range(m+1)] for j in range(n+1)]
def f(x,y):
    def g(u,v):
        if u == 0:
            return 1
        elif v == 0:
            return 1
        elif v == 1:
            return u
        elif u == 1:
            return 1
        elif memo[u][v] != 0:
            return memo[u][v]
        else:
            memo[u][v] = sum([g(u-1,i) for i in range(v+1)])
            return memo[u][v]
    return g(x,y)
# M を素因数分解
def h(x):
    t = x
    d = {}
    for i in range(2,x):
        if i*i > x:
            break
        if t % i != 0:
            continue
        if t % i == 0:
            ind = 0
            while t % i == 0:
                t = t // i
                ind += 1
            d[i] = ind
    if t != 1:
        d[x] = 1
    return d

res = 1
for i in h(m):
    res = (res *  f(n,h(m)[i])) % INF

print(res)

Fixed submission:
n,m = map(int,input().split())
INF = 10**9+7
inv = {}
inv[0] = 1
inv[1] = 1
def p(x):
    if x in inv:
        return inv[x]
    else:
        inv[x] = ((-1)* p(INF%x) * (INF//x))% INF
        return inv[x]
# n H i
l = [1] * 31
l[1] = n 
for i in range(2,31):
    l[i] = ((n+i-1)*l[i-1]*p(i))%INF
# M を素因数分解
def h(x):
    t = x
    d = {}
    for i in range(2,x):
        if i*i > x:
            break
        if t % i != 0:
            continue
        if t % i == 0:
            ind = 0
            while t % i == 0:
                t = t // i
                ind += 1
            d[i] = ind
    if t != 1:
        d[x] = 1
    return d

res = 1
for i in h(m):
    res = (res *  l[h(m)[i]]) % INF

print(res)