Bobby's Bet

Interview

Time limit2sMemory limit256 MB

Summary

Decide whether a bet pays off by computing the binomial chance of rolling at least R on at least X of Y rolls and comparing it to the odds W.

Level: Easy3 of 10
Topics: Probability, Combinatorics, Math
Solved: No attempts yet

Problem

Bobby and Betty have a bet. Betty bets that Bobby cannot roll an $S$ sided die, whose faces show $1$ through $S$ , and get a value of at least $R$ on at least $X$ of $Y$ rolls. Betty owns dice with different numbers of sides $S$ , and every one of them is fair, so on a given die each face is equally likely. To watch statistically rare events while still giving Bobby a reason to play, Betty offers $W$ to $1$ odds on every round.

For example, suppose Betty bets $1$ bitcoin that Bobby cannot roll at least a $5$ on a $6$ sided die at least two times out of three, at odds of $3$ to $1$ . If Bobby does it, Betty pays him $3$ times his original bet, that is $3$ bitcoins.

Should Bobby take the bet? In other words, is his expected return greater than his original bet?

Input

The first line contains the number of test cases $N$ ( $1 \le N \le 10000$ ).

Each of the next $N$ lines contains five integers $R$ , $S$ , $X$ , $Y$ and $W$ , separated by spaces. The 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 test case, print yes on its own line if Bobby's expected return is greater than his bet, and no otherwise.

Bobby is risk averse and does not bet when his expected return equals his bet.

Examples2

Example 1
Input
```
2
5 6 2 3 3
5 6 2 3 4
```
Expected output
```
no
yes
```

Example 2

Input

3
2 2 9 10 100
1 2 10 10 1
1 2 10 10 2

Expected output

yes
no
yes