def get_factorials(max, mod=None):
    """
    階乗 0!, 1!, 2!, ..., max!
    :param int max:
    :param int mod:
    """
    ret = [1]
    n = 1
    if mod:
        for i in range(1, max + 1):
            n *= i
            n %= mod
            ret.append(n)
    else:
        for i in range(1, max + 1):
            n *= i
            ret.append(n)
    return ret


def mod_invs(max, mod):
    """
    逆元 0, 1/1, 1/2, 1/3, ..., 1/max
    :param int max:
    :param int mod:
    """
    invs = [1] * (max + 1)
    invs[0] = 0
    for x in range(2, max + 1):
        invs[x] = (-(mod // x) * invs[mod % x]) % mod
    return invs


def factorial_invs(max, mod):
    """
    階乗 0!, 1!, 2!, ..., max! の逆元
    :param int max:
    :param int mod:
    """
    ret = [1]
    r = 1
    for inv in mod_invs(max, mod)[1:]:
        r = r * inv % mod
        ret.append(r)
    return ret


class Combination:
    def __init__(self, max, mod):
        """
        :param int max:
        :param int mod: 3 以上の素数であること
        """
        self._factorials = get_factorials(max, mod)
        self._finvs = factorial_invs(max, mod)
        self._mod = mod

    def ncr(self, n, r):
        """
        :param int n:
        :param int r:
        :rtype: int
        """
        if n < r:
            return 0
        return self._factorials[n] * self._finvs[r] % self._mod * self._finvs[n - r] % self._mod


if __name__ == '__main__':
    assert Combination(5, 10 ** 9 + 7).ncr(5, 3) == 10
    assert Combination(5, 10 ** 9 + 7).ncr(5, 1) == 5
    assert Combination(5, 7).ncr(5, 3) == 3
