from functools import lru_cache


@lru_cache(maxsize=1000000)
def possible_sums(n, n_orig, d):
    if d == n_orig:
        return 0
    if n == 0:
        return 1
    if n < 0:
        return 0
    if d > n:
        return 0
    return possible_sums(n - d, n_orig, d) + possible_sums(n, n_orig, d + 1)


def euler_076():
    return possible_sums(100, 100, 1)


if __name__ == "__main__":
    print("e076.py: " + str(euler_076()))
    assert(euler_076() == 190569291)