A13421 | Nastya and Rice

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 $x_i$ $(a - b \leq x_i \leq a + b)$ , and in total they weigh from $c - d$ to $c + d$ , inclusive ( $c - d \leq \sum\limits_{i=1}^{n}{x_i} \leq c + d$ ).

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

The next $t$ lines contain descriptions of the test cases, each line contains $5$ integers: $n$ $(1 \leq n \leq 1000)$ — the number of grains that Nastya counted and $a, b, c, d$ $(0 \leq b < a \leq 1000, 0 \leq d < c \leq 1000)$ — 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 $c + d$ ).

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 $c + d$ .