GCD!

The greatest common divisor (GCD) of two natural numbers is the largest natural number that divides both of them without a remainder. For example, the greatest common divisor of $8$ and $12$ is $\gcd(8, 12) = 4$, because $4$ is the largest integer that divides both $8$ and $12$. (The common divisors of $8$ and $12$ are $1, 2, 4$.)

The factorial of a natural number is the product of every positive integer less than or equal to it. For example, the factorial of $5$ is $5! = 1 \times 2 \times 3 \times 4 \times 5 = 120$. (By definition, $0! = 1$.)

Given two numbers $n$ and $k$, write a program that computes the greatest common divisor of $n!$ and $k$. For example, if $n = 3$ and $k = 10$, then $\gcd(n!, k) = \gcd(3!, 10) = \gcd(6, 10) = 2$.

The input consists of several lines. Each line contains two integers $n$ and $k$ separated by a space, and the input continues until the end of the file. ($0 \le n \le 1{,}000{,}000{,}000$, $1 \le k \le 1{,}000{,}000{,}000$)

For each line of the input, print the greatest common divisor of $n!$ and $k$ on its own line.