#### Start

2019-03-02 09:00 AKST

## NAIPC 2019

#### End

2019-03-02 14:00 AKST
The end is near!
Contest is over.
Not yet started.
Contest is starting in -632 days 10:02:14

5:00:00

0:00:00

# Problem CCost of Living

A newspaper columnist recently wrote a column comparing Disneyland’s price increases to other things in the economy; e.g., If gasoline were to have increased at the same rate as Disneyland’s admission since 1990, it would cost $\$ 6.66$per gallon. Consider the prices of a number of commodities over a number of consecutive years. There is an inflation rate ($\operatorname {inflation}(x){>}0$) for year$x$to the next year ($x{+}1$). Also, each commodity$A$has a modifier ($\operatorname {modifier}(A){>}0$) that is fixed for that commodity. So, for commodity$A$in year$x{+}1$:$\operatorname {price}(A,x{+}1)\! =\! \operatorname {price}(A,x)\cdot \operatorname {inflation}(x)\cdot \operatorname {modifier}(A)$Unfortunately, the modifiers are unknown, and some of the prices and inflation rates are unknown. Given some inflation rates, the prices for a number of commodities over a number of consecutive years, and some queries for prices for certain commodities in certain years, answer the queries. ## Input Each test case will begin with a line with three space-separated integers$y$($1{\le }y\! \le \! 10$),$c$($1{\le }c{\le }100$), and$q$($1\! \le \! q\! \le \! y{\cdot }c$), where$y$is the number of consecutive years,$c$is the number of commodities, and$q$is the number of queries to answer. Each of the next$y\! -\! 1$lines will contain a single real number$r$($1.0\! \le \! r\! \le \! 1.5$, or$r\! =\! -1.0$), which are the inflation rates. A value of$-1.0$indicates that the inflation rate is unknown. The first inflation rate is the change from year$1$to year$2$, the second from year$2$to year$3$, and so on. Known inflation rates will conform to the limits specified; unknown but uniquely determinable inflation rates may not, and are only guaranteed to be strictly greater than zero. Each of the next$y$lines will describe one year’s prices. They will contain$c$space-separated real numbers$p$($1.0\! <\! p\! <\! 1\, 000\, 000.0$, or$p\! =\! -1.0$), which indicate the price of that commodity in that year. A value of$-1.0$indicates that the price is unknown. Each of the next$q$lines will contain two space-separated integers$a$($1\! \le \! a\! \le \! c$) and$b$($1\! \le \! b\! \le \! y$), which represent a query for the price of commodity$a$in year$b$. All queries will be distinct. All prices that can be uniquely determined will be strictly greater than zero and strictly less than$1\, 000\, 000.0$. Values for prices and inflation rates in the input may not be exact, but will be accurate to$10$decimal places. All real values contain no more than$10$digits after the decimal point. ## Output Produce$q$lines of output. Each line should contain a single real number, which is the price of the given commodity in the given year, or$-1.0$if it cannot be determined. Answer the queries in the order that they appear in the input. Your answers will be accepted if they are within an absolute or relative error of$10^{-4}\$.

Sample Input 1 Sample Output 1
4 2 2
1.3333333333
1.2500000000
-1
3.00 -1
4.00 8.00
5.00 10.00
-1 11.00
2 1
1 4

6.0000000000
5.5000000000