Buggy python submission (verdict: Runtime Error):
import sys

MOD = 10 ** 9 + 7

def main():
    n, m = [int(s) for s in input().split()]
    print(solve(m, n))

def solve(m, n):
    factors = list(get_prime_factors(m))
    h = max(c for f, c in factors)

    table = dict()
    table[1] = [1 for _ in range(h + 1)]

    i = 1
    while i < n:
        j = n & (i - 1)
        table[i * 2] = [0 for _ in range(h + 1)]
        if n & i != 0 and j != 0:
            table[i + j] = [0 for _ in range(h + 1)]
        for x in range(h + 1):
            for y in range(h + 1 - x):
                table[i * 2][x + y] = (table[i * 2][x + y] + table[i][x] * table[i][y]) % MOD
                if n & i != 0 and j != 0:
                    table[i + j][x + y] = (table[i + j][x + y] + table[i][x] * table[j][y]) % MOD

        if n & i == 0:
            del table[i]
        if n & i != 0 and j != 0:
            del table[i]
            del table[j]

        i *= 2

    ans = 1
    for f, c in factors:
        ans = ans * table[n][c] % MOD
    return ans

def get_prime_factors(n):
    import itertools

    m = n
    for i in itertools.count(2):
        if i * i > m:
            break

        c = 0
        while True:
            x, y = divmod(m, i)
            if y != 0:
                break
            c += 1
            m = x
        if c != 0:
            yield i, c

    if m != 1:
        yield m, 1


main()


Fixed submission:
import sys

MOD = 10 ** 9 + 7

def main():
    n, m = [int(s) for s in input().split()]
    print(solve(m, n))

def solve(m, n):
    factors = list(get_prime_factors(m))
    h = max((c for f, c in factors), default=0)

    table = dict()
    table[1] = [1 for _ in range(h + 1)]

    i = 1
    while i < n:
        j = n & (i - 1)
        table[i * 2] = [0 for _ in range(h + 1)]
        if n & i != 0 and j != 0:
            table[i + j] = [0 for _ in range(h + 1)]
        for x in range(h + 1):
            for y in range(h + 1 - x):
                table[i * 2][x + y] = (table[i * 2][x + y] + table[i][x] * table[i][y]) % MOD
                if n & i != 0 and j != 0:
                    table[i + j][x + y] = (table[i + j][x + y] + table[i][x] * table[j][y]) % MOD

        if n & i == 0:
            del table[i]
        if n & i != 0 and j != 0:
            del table[i]
            del table[j]

        i *= 2

    ans = 1
    for f, c in factors:
        ans = ans * table[n][c] % MOD
    return ans

def get_prime_factors(n):
    import itertools

    m = n
    for i in itertools.count(2):
        if i * i > m:
            break

        c = 0
        while True:
            x, y = divmod(m, i)
            if y != 0:
                break
            c += 1
            m = x
        if c != 0:
            yield i, c

    if m != 1:
        yield m, 1


main()

Buggy python submission (verdict: Runtime Error):
MOD = 10 ** 9 + 7

def main():
    n, m = [int(s) for s in input().split()]
    print(solve(m, n))

def solve(m, n):
    factors = list(get_prime_factors(m))
    h = max(c for f, c in factors)

    table = dict()
    table[1] = [1 for _ in range(h + 1)]

    i = 1
    while i < n:
        j = n & (i - 1)
        table[i * 2] = [0 for _ in range(h + 1)]
        if j != 0:
            table[i + j] = [0 for _ in range(h + 1)]
        for x in range(h + 1):
            for y in range(h + 1 - x):
                table[i * 2][x + y] = (table[i * 2][x + y] + table[i][x] * table[i][y]) % MOD
                if j != 0:
                    table[i + j][x + y] = (table[i + j][x + y] + table[i][x] * table[j][y]) % MOD
        i *= 2

    ans = 1
    for f, c in factors:
        ans = ans * table[n][c] % MOD
    return ans

def get_prime_factors(n):
    import itertools

    m = n
    for i in itertools.count(2):
        if i * i > m:
            break

        c = 0
        while True:
            x, y = divmod(m, i)
            if y != 0:
                break
            c += 1
            m = x
        if c != 0:
            yield i, c

    if m != 1:
        yield m, 1


main()


Fixed submission:
import sys

MOD = 10 ** 9 + 7

def main():
    n, m = [int(s) for s in input().split()]
    print(solve(m, n))

def solve(m, n):
    factors = list(get_prime_factors(m))
    h = max((c for f, c in factors), default=0)

    table = dict()
    table[1] = [1 for _ in range(h + 1)]

    i = 1
    while i < n:
        j = n & (i - 1)
        table[i * 2] = [0 for _ in range(h + 1)]
        if n & i != 0 and j != 0:
            table[i + j] = [0 for _ in range(h + 1)]
        for x in range(h + 1):
            for y in range(h + 1 - x):
                table[i * 2][x + y] = (table[i * 2][x + y] + table[i][x] * table[i][y]) % MOD
                if n & i != 0 and j != 0:
                    table[i + j][x + y] = (table[i + j][x + y] + table[i][x] * table[j][y]) % MOD

        if n & i == 0:
            del table[i]
        if n & i != 0 and j != 0:
            del table[i]
            del table[j]

        i *= 2

    ans = 1
    for f, c in factors:
        ans = ans * table[n][c] % MOD
    return ans

def get_prime_factors(n):
    import itertools

    m = n
    for i in itertools.count(2):
        if i * i > m:
            break

        c = 0
        while True:
            x, y = divmod(m, i)
            if y != 0:
                break
            c += 1
            m = x
        if c != 0:
            yield i, c

    if m != 1:
        yield m, 1


main()

Buggy python submission (verdict: Time Limit Exceeded):
M = 10 ** 9 + 7

def main():
    n, m = [int(s) for s in input().split()]

    print(solve(m, n))

def solve(m, n):

    fs = list(factors(m))
    table = dict()
    table[1] = dict()

    for f in fs:
        table[1][f] = 1

    h = 1
    for _ in range(1, n.bit_length()):
        row = dict()
        for f in fs:
            for g in fs:
                if f * g > m:
                    break
                row[f * g] = (row.get(f * g, 0) + table[h][f] * table[h][g]) % M
        table[h * 2] = row
        h *= 2

    prev = { 1: 1 }
    result = None
    h = 1
    for _ in range(n.bit_length()):
        if n & h:
            result = dict()
            for f in prev.keys():
                for g in table[h].keys():
                    if f * g <= m:
                        result[f * g] = (result.get(f * g, 0) + prev[f] * table[h][g]) % M
            prev = result
        h *= 2
    return result[m]

def factors(n):
    import itertools

    tail = []
    for i in itertools.count(1):
        if i * i > n:
            break

        m, r = divmod(n, i)
        if r == 0:
            yield i
            if m != i:
                tail.append(m)
    
    for i in tail[::-1]:
        yield i

main()


Fixed submission:
import sys

MOD = 10 ** 9 + 7

def main():
    n, m = [int(s) for s in input().split()]
    print(solve(m, n))

def solve(m, n):
    factors = list(get_prime_factors(m))
    h = max((c for f, c in factors), default=0)

    table = dict()
    table[1] = [1 for _ in range(h + 1)]

    i = 1
    while i < n:
        j = n & (i - 1)
        table[i * 2] = [0 for _ in range(h + 1)]
        if n & i != 0 and j != 0:
            table[i + j] = [0 for _ in range(h + 1)]
        for x in range(h + 1):
            for y in range(h + 1 - x):
                table[i * 2][x + y] = (table[i * 2][x + y] + table[i][x] * table[i][y]) % MOD
                if n & i != 0 and j != 0:
                    table[i + j][x + y] = (table[i + j][x + y] + table[i][x] * table[j][y]) % MOD

        if n & i == 0:
            del table[i]
        if n & i != 0 and j != 0:
            del table[i]
            del table[j]

        i *= 2

    ans = 1
    for f, c in factors:
        ans = ans * table[n][c] % MOD
    return ans

def get_prime_factors(n):
    import itertools

    m = n
    for i in itertools.count(2):
        if i * i > m:
            break

        c = 0
        while True:
            x, y = divmod(m, i)
            if y != 0:
                break
            c += 1
            m = x
        if c != 0:
            yield i, c

    if m != 1:
        yield m, 1


main()

Buggy python submission (verdict: Time Limit Exceeded):
M = 10 ** 9 + 7

def main():
    n, m = [int(s) for s in input().split()]

    print(solve(m, n))

def solve(m, n):
    prev = dict()

    fs = list(factors(m))
    for f in fs:
        prev[f] = 1

    for _ in range(n - 1):
        row = dict()
        for f in fs:
            s = 0
            for g in factors(f):
                s = (s + prev[f // g]) % M
            row[f] = s
        prev = row

    return prev[m]

def factors(n):
    import itertools

    tail = []
    for i in itertools.count(1):
        if i * i > n:
            break

        m, r = divmod(n, i)
        if r == 0:
            yield i
            if m != i:
                tail.append(m)
    
    for i in tail[::-1]:
        yield i

main()


Fixed submission:
import sys

MOD = 10 ** 9 + 7

def main():
    n, m = [int(s) for s in input().split()]
    print(solve(m, n))

def solve(m, n):
    factors = list(get_prime_factors(m))
    h = max((c for f, c in factors), default=0)

    table = dict()
    table[1] = [1 for _ in range(h + 1)]

    i = 1
    while i < n:
        j = n & (i - 1)
        table[i * 2] = [0 for _ in range(h + 1)]
        if n & i != 0 and j != 0:
            table[i + j] = [0 for _ in range(h + 1)]
        for x in range(h + 1):
            for y in range(h + 1 - x):
                table[i * 2][x + y] = (table[i * 2][x + y] + table[i][x] * table[i][y]) % MOD
                if n & i != 0 and j != 0:
                    table[i + j][x + y] = (table[i + j][x + y] + table[i][x] * table[j][y]) % MOD

        if n & i == 0:
            del table[i]
        if n & i != 0 and j != 0:
            del table[i]
            del table[j]

        i *= 2

    ans = 1
    for f, c in factors:
        ans = ans * table[n][c] % MOD
    return ans

def get_prime_factors(n):
    import itertools

    m = n
    for i in itertools.count(2):
        if i * i > m:
            break

        c = 0
        while True:
            x, y = divmod(m, i)
            if y != 0:
                break
            c += 1
            m = x
        if c != 0:
            yield i, c

    if m != 1:
        yield m, 1


main()