문제1442--GCD!

1442: GCD!

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문제 설명

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!

입력 설명

Each line contains two integers, n (0 <= n <= 1,000,000,000) and k (1 <= k <= 1,000,000,000) respectively.

출력 설명

For each line of input, output one line containing the GCD of n! and k.

입력 예시 Copy

3 10
10 240
12 364
100 2351
629 163547

출력 예시 Copy

2
240
28
1
67

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