In a card game consisting of $r$ rounds, you have $n$ cards. Each card has a score $a_i$, and the probability of successfully using card $i$ is $p_i$. In each round:
- Start from the first card ($1, 2, ..., n$).
- If the card is already used, move to the next card.
- If the card is unused:
- With probability $p_i$, the card is successfully used, and the round ends.
- With probability $1-p_i$, the card fails to be used, so move to the next card.
- If all cards are exhausted without success, proceed to the next round.
You are tasked to calculate the expected value of the total score obtained after $r$ rounds.
### Input
- The first line contains an integer $T$, the number of test cases.
- For the next $T$ datasets:
- The first line contains two integers $n, r$.
- The next $n$ lines each contain two numbers $p_i, a_i$.
### Output
- Print a floating-point number representing the expected total score, rounded to at least 6 decimal places.
### Constraints
- $1 \le T \le 500$.
- $1 \le n \le 222$.
- $1 \le r \le 133$.
- $0 < p_i < 1$.
- $1 \le a_i \le 1000$.
### Sample Test
Input:
```
1
3 2
0.4000 2
0.3000 3
0.8000 1
```
Output
```
3.0814240000
```
