Bobby and Betty have a bet. Betty bets Bobby that he cannot
roll an $S$sided die
(having values $1$ through
$S$) and obtain a value
$\ge R$ on at least
$X$ out of $Y$ rolls. Betty has a variety of dice
with different numbers of sides $S$, and all her dice are fair (for a
given die, each side’s outcome is equally likely). In order to
observe statistically rare events while still giving Bobby a
reason to bet, Betty offers to pay Bobby $W$ times his bet on each encounter.
For example, suppose Betty bets Bobby $1$ bitcoin that he can’t roll at
least a $5$ on a
$6$sided die at least two
out of three times; if Bobby does, she would give him
$W=3$ times his initial
bet (i.e. she would give him $3$ bitcoins). Should Bobby take the
bet (is his expected return greater than his original bet)?
Input
Input begins with an integer $1 \le N \le 10\, 000$, representing
the number of cases that follow. The next $N$ lines each contain five integers,
$R$, $S$, $X$, $Y$, and $W$. Their limits are $1 \le R \le S \le 20$, $1 \le X \le Y \le 10$, and
$1 \le W \le 100$.
Output
For each case, output “yes” if Bobby’s expected return is
greater than his bet, or “no” otherwise. Bobby is somewhat risk
averse and does not bet if his expected return is equal to his
bet.
Sample Input 1 
Sample Output 1 
2
5 6 2 3 3
5 6 2 3 4

no
yes

Sample Input 2 
Sample Output 2 
3
2 2 9 10 100
1 2 10 10 1
1 2 10 10 2

yes
no
yes
