模为10^9 +7的两个二项式系数的GCD

def binomial_coefficient(n, k, p):
    if k > n:
        return 0
    if k == 0 or k == n:
        return 1
    
    # Calculate binomial coefficient using Lucas theorem
    result = 1
    while n > 0 and k > 0:
        n0 = n % p
        k0 = k % p
        if n0 < k0:
            return 0
        result = (result * C(n0, k0, p)) % p
        n //= p
        k //= p
    
    return result

def C(n, k, p):
    # Calculate binomial coefficient using dynamic programming
    dp = [[0] * (k+1) for _ in range(n+1)]
    for i in range(n+1):
        for j in range(min(i, k)+1):
            if j == 0 or j == i:
                dp[i][j] = 1
            else:
                dp[i][j] = (dp[i-1][j-1] + dp[i-1][j]) % p
    return dp[n][k]

# Example usage
n = 10
k = 5
p = 10**9 + 7
gcd = binomial_coefficient(n, k, p)
print(gcd)