BDOI16B - Beautiful Factorial Game


The statement of this problem is very simple. Given two number n and k, you need to find the maximum power of k (i.e. x) such that n! % kx = 0. Here n! is the notation of n factorial. If you are not familiar with the notation,

n! = 1 * 2 * 3 * 4 * 5 * 6 ... * n

Input

First line of the input will contain an integer t (1 ≤ t ≤ 20) denoting the number of test case. The next t lines contain two integer number n and k as described above.

Constraints

For easy version, 1 ≤ n ≤ 10, 2 ≤ k ≤ 10

For harder version, 1 ≤ n ≤ 100000000, 2 ≤ k ≤ 100000000

Output

For each test case, print “Case t: x” where t is the test case number and x is the maximum power of k for which n! % kx = 0.

Example

Input:
2
5 2
1000 2

Output:
Case 1: 3
Case 2: 994

Explanation

In the first test case, n = 5 and k = 2. So, n! = 120.

  • 120 % 20 = 0
  • 120 % 21 = 0
  • 120 % 22 = 0
  • 120 % 23 = 0
  • 120 % 24 = 8
  • 120 % 25 = 24
  • 120 % 26 = 56
  • 120 % 27 = 120

So, the answer should be 3.

Problem Setter: Rakibul Islam


hide comments
cyclic_func: 2017-01-07 10:00:13

C.a

Last edit: 2017-01-07 10:08:05
aman224: 2016-11-28 14:37:05

AC!!!

Last edit: 2016-11-29 00:03:37
[Lakshman]: 2016-10-07 22:09:08

There is already a problem with better constraints http://www.spoj.com/problems/GCPC11A/

wisfaq: 2016-10-07 14:59:35

For easy version, 1 <= n <= 10, 2 <= k <= 10
For harder version, 1 <= n <= 100000000, 2 <= k <= 100000000

Which of the two do we have here?

Sushovan Sen: 2016-10-06 20:42:18

Test cases are very weak. Please add some more.


Added by:Rezwan
Date:2016-10-05
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU
Resource:Bangladesh Olympiad on Informatics 2016 National; Problem Setter: Rakibul Islam