The Snail

Time limit1sMemory limit128 MB

Summary

Simulate a snail that climbs a bit less each day and slides a fixed distance each night, and report whether it escapes or falls back first.

Level: Easy3 of 10
Topics: Implementation, Simulation, Math
Solved: No attempts yet

Problem

A snail is at the bottom of a well that is $H$ feet deep and wants to climb to the top. During the day, while the sun is up, the snail climbs upward; at night, while it sleeps, it slides back down.

On the first day the snail climbs $U$ feet. However, the snail grows tired, so it climbs a little less each day. Specifically, on day $n$ the snail climbs $U - (n-1)\times U \times \dfrac{F}{100}$ feet. (The distance lost to fatigue is always $F\%$ of the first day's climbing distance.) If this value is negative, the snail does not climb at all that day (it climbs a distance of 0). No matter how far it climbed during the day, at night the snail always slides down $D$ feet.

The moment the snail's height first exceeds the well's height of $H$ feet, it leaves the well. Conversely, if after sliding at night its height becomes negative, the snail has slid back to the bottom of the well and fails. (A day consists of a period of sunlight followed by a period of darkness.)

For example, when $H=6,\ U=3,\ D=1,\ F=10$ , the snail leaves the well on the third day, as shown in the table below.

Day	Initial Height	Distance Climbed	Height After Climbing	Height After Sliding
1	0′	3′	3′	2′
2	2′	2.7′	4.7′	3.7′
3	3.7′	2.4′	6.1′	–

Depending on the parameters, the snail will eventually either leave the well (its height exceeds $H$ ) or slide back to the bottom (its height becomes negative). Determine which happens first, and on which day.

Input

The input consists of one or more test cases, each on a line by itself. Each line contains four integers $H,\ U,\ D,\ F$ separated by single spaces.

$H$ : the height of the well in feet
$U$ : the distance the snail climbs during the day in feet
$D$ : the distance the snail slides down at night in feet
$F$ : the fatigue factor expressed as a percentage

A line with $H = 0$ signals the end of the input and is not processed. Otherwise all four integers are between $1$ and $100$ , inclusive. The snail never climbs a negative distance: if fatigue drops the climbing distance below zero, the snail does not climb at all that day. Regardless of how far it climbed, it always slides $D$ feet at night.

Output

For each test case, output a single line.

If the snail leaves the well (success), print:

success on day <n>

If the snail slides back to the bottom (failure), print:

failure on day <n>

where <n> is the number of the day on which the event occurs.

Examples3

Example 1

Input

Expected output

success on day 3
failure on day 4
failure on day 7
failure on day 68
success on day 20
failure on day 2

Example 2
Input
```
2 3 1 10
0 0 0 0
```
Expected output
```
success on day 1
```
Example 3
Input
```
3 3 1 10
0 0 0 0
```
Expected output
```
success on day 2
```