# Practice on Toph

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# Ada in Dreamland

By reborn · Limits 1s, 256 MB

Ada is wondering in her dreamland. Her dreamland consists of n spots. She has this weird machine with her that shows real numbers. And whenever she goes from spot u to v, if she can (by following a trail), the value shown in the machine gets multiplied with cuv which is another weird value for each trail that exists between two spots.

Ada is currently in spot 1 and her machine currently reads value d. She wants to go to spot n in a way so that the machine shows zero when she reaches n. Is that possible?

Please note that, Ada can visit a spot multiple times if it helps her.

Ada’s machine displays zero when the value is either zero or tends to be zero. To say that x tends to zero is to say that x varies in such a way that its numerical value becomes and remains less than any positive number that we may choose, no matter how small.

## Input

First line contains two integers and one positive real number n (2 ≤ n ≤ 103), m (0 ≤ m ≤ min(10^5, n(n-1))), d (d ≤ 106); the number of spots, the number of trails, the initial reading of the machine respectively.

Each of the next m lines contains two integers u, v (1 ≤ u, v ≤ n) and a positive real number cuv (0 < cuv); which corresponds to a trail from spot u to spot v with the multiplier cuv.

cuv and d will have exactly 2 digits after the decimal place.

Note that the trails are unidirectional. Also, there will be no trail from a spot to itself. And there exists at most one trail from a spot u to v.

## Output

If Ada can not reach spot n anyhow, please output “Unreachable” on a line. Else, print “Yes” if she can obtain zero at the machine reading after arriving in spot n. Print “No” otherwise.

## Sample

InputOutput
```5 5 1.00
1 2 0.10
2 3 7.00
2 4 2.00
4 3 0.90
3 5 0.05
```
```No
```

There are two ways to go to 5 from 1:

A. 1-2-3-5 yields a value of 1 × 0.10 × 7.00 × 0.05 = 0.035.

B. 1-2-4-3-5 yields a value of 1 × 0.10 × 2.00 × 0.90 × 0.05 = 0.09.

None of them yields 0.

### Statistics

25% Solution Ratio

NirjhorEarliest, 4M ago

EgorKulikovFastest, 0.2s

NirjhorLightest, 4.1 MB

tmwilliamlin168Shortest, 1142B