Problem B
Soot Sprite Sprinklers
The latest decree from the Castle in the Sky Homeowners Association (CSHOA) announces a new regulation where you are required to water your garden with at least $w$ gallons of water between every inspection, which comes around every $p$ minutes. You already have a working watering schedule: the Soot Sprite Sprinklers are configured to be on a $(t + b)$-minute cycle, where they water your garden at $r$ gallons of water per minute for $t$ minutes and then take a $b$-minute break. Coincidentally, the next watering cycle begins exactly on the next CSHOA inspection, when the new regulation will begin to take effect. You are lazy and would rather not change the sprinkler configurations if the current watering schedule already complies with the new regulation. Print “The CSHOA decrees are as murky as the Forest Spirit” if you have to change the configuration and “Soot Sprites sing a lullaby” otherwise.
Input
The only line of input consists of five space-separated integers $w$, $p$, $t$, $b$, and $r \: (1 \leq w, p, t, b, r \leq 10^9)$. $w$ is the required number of gallons of water per inspection. $p$ is the inspection interval in minutes. $t$ is the watering time per watering cycle in minutes. $b$ is the break time per watering cycle in minutes. $r$ is the rate at which the Soot Sprite Sprinklers water your garden in gallons per minute.
Output
Output a single line containing “The CSHOA decrees are as murky as the Forest Spirit” if you have to change the configuration and “Soot Sprites sing a lullaby” otherwise.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 6 2 2 1 |
The CSHOA decrees are as murky as the Forest Spirit |
| Sample Input 2 | Sample Output 2 |
|---|---|
5 5 2 1 2 |
Soot Sprites sing a lullaby |
