Scattered Rice Coding Question-Codeforces Rated 900

Problem Statement :

Nastya just made a huge mistake and dropped a whole package of rice on the floor. Mom will come soon. If she sees this, then Nastya will be punished.

In total, Nastya dropped n grains. Nastya read that each grain weighs some integer number of grams from a−b to a+b, inclusive (numbers a and b are known), and the whole package of n grains weighs from c−d to c+d grams, inclusive (numbers c and d are known). The weight of the package is the sum of the weights of all n grains in it.

Help Nastya understand if this information can be correct. In other words, check whether each grain can have such a mass that the i-th grain weighs some integer number xi (a−b≤xi≤a+b), and in total, they weigh from c−d to c+d, inclusive.

Input Format:

The input consists of multiple test cases. The first line contains a single integer t (1≤t≤1000) — the number of test cases.

The next t lines contain descriptions of the test cases, each line contains 5 integers: n (1≤n≤1000) — the number of grains that Nastya counted and a,b,c,d (0≤b<a≤1000,0≤d<c≤1000) — numbers that determine the possible weight of one grain of rice (from a−b to a+b) and the possible total weight of the package (from c−d to c+d).

Output Format:

For each test case given in the input print “Yes”, if the information about the weights is not inconsistent, and print “No” if n grains with masses from a−b to a+b cannot make a package with a total mass from c−d to c+d.



Explanation of given Test Cases :


We can get any weight of all grains from n(a−b) to n(a+b), so we need to check that the segments [n(a−b),n(a+b)] and [c−d,c+d] intersect.


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