The greatest common divisor of two numbers is defined as the largest integer that divides both numbers without leaving any reminder. For example, the greatest common divisor of 8 and 12, written as GCD(8,12) is 4, as 4 is the largest integer that divides both 8 and 12 (the common divisors of 8 and 12 are 1, 2, and 4).
Meanwhile, the factorial of a natural number is the product of all positive integers less than or equal to that number. For example, the factorial of 5, written as 5! is 1*2*3*4*5, which equals to 120. By convention, 0! is 1.
Given two integers,
n and
k, you should find the greatest common divisor of
n! and
k. For example, if
n = 3 and
k = 10, then GCD(
n!,
k) = GCD(3!,10) = GCD(1*2*3,10) = GCD(6,10) = 2. Write a program to find this number!
Input
Each line contains two integers,
n (0 <=
n <= 1,000,000,000) and
k (1 <=
k <= 1,000,000,000) respectively.
Output
For each line of input, output one line containing the GCD of
n! and
k.
Sample Input
3 10
10 240
12 364
100 2351
629 163547
Sample Output
2
240
28
1
67