HDU 6624 fraction 辗转相除法_fraction common exact-优快云博客

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fraction

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 467 Accepted Submission(s): 249

Problem Description

Many problems require printing the probability of something. Moreover, it is common that if the answer is ab , you should output a×b−1(modp) (p is a prime number). In these problems, you cannot know the exact value of the probability. It's so confusing!!! Now, we want to reverse engineer the exact probability from such calculated output value x . We do so by guessing the probability is the one with the minimum b such that a×b−1=x(modp) . Now we invite you to solve this problem with us!

You are given two positive integers p and x , where p is a prime number.

Please find the smallest positive integer b such that there exist some positive integer a satisfying a<b and a≡bx(modp) .

Input

The first line contains an integer T indicating there are T tests. Each test consists of a single line containing two integers: p,x .

* 1≤T≤2×105

* 3≤p≤1015

* p is a prime

* 1<x<p

Output

For each test, output a line containing a string represents the fraction ab using the format "a/b" (without quotes).

Sample Input

3 11 7 998244353 554580197 998244353 998244352

Sample Output

2/5 8/9 499122176/499122177

$\frac{a}{b}\equiv x(mod \ p)$