from functools import reduce

target = [19,19]
start = [0,0]

side = 2

count = 0
# 2: 6
# 3: 20
# 4: 70
# 5: 252
# 6: 924

def recurse(x, y):
    global count
    # print(x, y)

    if (x == side and y == side):
        count += 1
        print('found', count)
        return

    if (x < side):
        # print('increasing x')
        recurse(x + 1, y)

    if (y < side):
        # print('increasing y')
        recurse(x, y + 1)

count = 0
def smarter_recurse(index, bits):
    # print(index, bits)
    global count

    if (index == 0):
        if (bits == 0):
            count += 1
        return;

    if (index - 1 >= bits):
        smarter_recurse(index-1, bits);

    if (bits > 0):
        smarter_recurse(index - 1, bits-1)

# side = 2

# smarter_recurse(side * 2, side)

def product(x, y):
    return x * y

# 10! / 5!^2
def do_it(slots, bits):
    numerator = reduce(product, list(range(slots + 1 - bits, slots + 1)))
    denomerator = reduce(product, list(range(1, bits + 1)))

    print(int(numerator / denomerator))


# smarter_recurse(8, 4)

# print(count)
# do_it(40, 20)

slots = 7
bits = 3
# smarter_recurse(slots, bits)

# print(count)

# do_it(slots, bits)
# do_it(7, 0)
do_it(7, 1)
do_it(7, 2)
do_it(7, 3)
do_it(7, 4)
do_it(7, 5)
do_it(7, 6)