CF1341A.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 ($c - d \leq \sum\limits_{i=1}^{n}{x_i} \leq c + d$).

娜斯佳刚刚犯了一个大错，把一整包大米全洒在了地上。妈妈很快就要回来了。如果她看到这一幕，娜斯佳就会受到惩罚。

总共，娜斯佳洒落了 $n$ 粒米。娜斯佳读到，每粒米的重量（单位：克）是一个介于 $a - b$ 到 $a + b$ 之间的整数（含端点）（其中 $a$ 和 $b$ 是已知的），而整包 $n$ 粒米的总重量则介于 $c - d$ 到 $c + d$ 克之间（含端点）（其中 $c$ 和 $d$ 是已知的）。整包米的重量等于所有 $n$ 粒米重量之和。

请帮娜斯佳判断这些信息是否可能成立。换句话说，请判断是否存在一种方式，为每粒米赋予一个质量 $x_i$，使得对每个 $i$ 都有 $x_i$ 为整数且满足 $a - b \leq x_i \leq a + b$，并且总重量满足 $c - d \leq \sum\limits_{i=1}^{n}{x_i} \leq c + d$。

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 $a, b, c, d$ $(0 \leq b \lt a \leq 1000, 0 \leq d \lt c \leq 1000)$ — 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 $c + d$).

输入包含多个测试用例。第一行包含一个整数 $t$（$1 \leq t \leq 1000$），表示测试用例的数量。

接下来的 $t$ 行描述各测试用例，每行包含 $5$ 个整数：$n$（$1 \leq n \leq 1000$）—— Nastya 数出的大米粒数；以及 $a, b, c, d$（$0 \leq b \lt a \leq 1000,\ 0 \leq d \lt c \leq 1000$）—— 用于确定单粒大米可能重量（范围为 $a - b$ 到 $a + b$）以及整包大米可能总重量（范围为 $c - d$ 到 $c + d$）的参数。

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 $c + d$.

对于输入中的每个测试用例，如果关于重量的信息不存在矛盾，则输出“Yes”；如果无法用 $n$ 粒质量在 $a - b$ 到 $a + b$ 之间的谷物组成总质量在 $c - d$ 到 $c + d$ 之间的包装，则输出“No”。

In the first test case of the example, we can assume that each grain weighs $17$ grams, and a pack $119$ grams, then really Nastya could collect the whole pack.

In the third test case of the example, we can assume that each grain weighs $16$ grams, and a pack $128$ grams, then really Nastya could collect the whole pack.

In the fifth test case of the example, we can be assumed that $3$ grains of rice weigh $2$, $2$, and $3$ grams, and a pack is $7$ grams, then really Nastya could collect the whole pack.

In the second and fourth test cases of the example, we can prove that it is impossible to determine the correct weight of all grains of rice and the weight of the pack so that the weight of the pack is equal to the total weight of all collected grains.

在示例的第一个测试用例中，我们可以假设每粒米重 $17$ 克，而一包米重 $119$ 克，那么娜斯佳确实可以恰好收集到整包米。

在示例的第三个测试用例中，我们可以假设每粒米重 $16$ 克，而一包米重 $128$ 克，那么娜斯佳确实可以恰好收集到整包米。

在示例的第五个测试用例中，我们可以假设 $3$ 粒米的重量分别为 $2$、$2$ 和 $3$ 克，而一包米重 $7$ 克，那么娜斯佳确实可以恰好收集到整包米。

在示例的第二个和第四个测试用例中，我们可以证明：不存在一组满足条件的、所有米粒的正确重量以及整包米的重量，使得整包米的重量等于所有已收集米粒的总重量。