You are given two integers N,CN,C and two integer sequences aa and bb of length NN. The sequences are indexed from 11 to NN.
Please solve the following equation for xx:
∑i=1N|ai⋅x+bi|=C∑i=1N|ai⋅x+bi|=C, where |v||v| means the absolute value of vv.
Input
The first line contains an integer TT indicating there are TT tests. Each test consists of N+1N+1 lines. The first line contains two integers N,CN,C. The ii-th line of following NN lines consists of two integers ai,biai,bi.
* 1≤T≤501≤T≤50
* 1≤N≤1051≤N≤105
* 1≤ai≤10001≤ai≤1000
* −1000≤bi≤1000−1000≤bi≤1000
* 1≤C≤1091≤C≤109
* only 55 tests with NN larger than 1000
Output
For each test, output one line. If there are an infinite number of solutions, this line consists only one integer −1−1. Otherwise, this line first comes with an integer mm indicating the number of solutions, then you must print mm fractions from the smallest to the largest indicating all possible answers. (It can be proved that all solutions can be written as fractions). The fraction should be in the form of "a/b" where a must be an integer, b must be a positive integer, and gcd(abs(a),b)=1gcd(abs(a),b)=1. If the answer is 00, you should output "0/1".