A Weighty Problem

You like to pay with coins, but you have a problem: you carry so much loose change that your pocket has grown too heavy. You have a plan to lighten it, and you need a program to carry it out.

Your next purchase costs $C$ cents. You will hand over some of your coins whose total value is at least $C$; if you overpay, the store gives you change. Choose which coins to spend so that the total weight of the coins left in your pocket afterward — the coins you did not spend, plus the coins the store hands back as change — is as small as possible.

When the store owes you $X$ cents it makes change greedily: it repeatedly gives you one coin of the largest denomination whose value is at most $X$, subtracts that value from $X$, and continues until $X$ reaches $0$. The store has an unlimited supply of every denomination.

There are $D$ denominations. Denomination $i$ has an integer value $V_i$ (in cents) and a weight $W_i$ (in grams). Exactly one denomination has value $1$, and no two denominations share a value.

You own $K$ coins; coin $j$ is of denomination $D_j$.

Constraints: $1 \le C \le 100000$, $1 \le D \le 100$, $1 \le K \le 100$, $1 \le V_i \le 2000$, $0 < W_i < 10$ (given to two decimal places), and $1 \le D_j \le D$.

The first line contains three integers $C$, $D$, and $K$: the cost of the purchase in cents, the number of coin denominations, and the number of coins you own.

Each of the next $D$ lines contains an integer $V_i$ and a real number $W_i$ (given to exactly two decimal places): the value in cents and the weight in grams of denomination $i$.

Each of the next $K$ lines contains one integer $D_j$: the 1-based denomination of the $j$-th coin you own.

If you can afford the purchase, print the minimum achievable total weight in grams, rounded to two decimal places (the answer is always an exact multiple of $0.01$). Otherwise, print too poor.

Suppose you own seven 5-cent coins and are buying something for 3 cents, with denominations of 1, 5, 10, and 20 cents weighing 1, 2, 1, and 9 grams respectively.

One optimal choice is to spend three 5-cent coins: the store then owes you 12 cents and returns one 10-cent coin and two 1-cent coins. Another is to spend four 5-cent coins: the store owes you 17 cents and returns one 10-cent coin, one 5-cent coin, and two 1-cent coins. Both leave $11.00$ grams in your pocket.