Задача Easy Trading

Описание

Frank is a professional stock trader for Advanced Commercial Markets Limited (ACM Ltd ). He likes “easy trading” — using a straightforward strategy to decide when to buy stock and when to sell it.

Frank has a database of historical stock prices for each day. He uses two integer numbers m and n (1 ≤ m < n ≤ 100) as parameters of his trading strategy. Every day he computes two numbers: P (m) — an average stock price for the previous m days, and P (n) — an average stock price for the previous n days. P (m) > P (n) is an indicator of the upward trend (traders call it bullish trend), and P (m) < P (n) is an indicator of the downward trend (traders call it bearish trend). In practice the values for P (m) and P (n) are never equal.

When a trend reverses from bearish to bullish it is a signal for Frank to buy stock. When a trend reverses from bullish to bearish it is a signal to sell.

Frank has different values for m and n in mind and he wants to backtest them using historical prices. He takes a set of k (n < k ≤ 10 000) historical prices p _i (0 < p _i < 100 for 1 ≤ i ≤ k). For each i (n ≤ i ≤ k) he computes P _i (m) and P _i (n) — an arithmetic average of p _i−m+1 . . . p _i and p _i−n+1 . . . p _i respectively.

Backtesting generates trading signals according to the following rules.

• If P _i (m) > P _i (n) there is a bullish trend for day i and a “BUY ON DAY i” signal is generated if i = n or there was a bearish trend on day i − 1.

• If P _i (m) < P _i (n) there is a bearish tread for day i and a “SELL ON DAY i” signal is generated if i = n or there was a bullish trend on day i − 1.

Your task is to write a program that backtests a specified strategy for Frank — you shall print a signal for the first tested day (day n) followed by the signals in increasing day numbers.

Формат входных данных

The first line of the input file contains three integer numbers m, n, and k. It is followed by k lines with stock prices for days 1 to k. Each stock price p _i is specified with two digits after decimal point. Prices in the input file are such that P _i (m) = P _i (n) for all i (n ≤ i ≤ k).

Формат выходных данных

Write to the output file a list of signals — one signal on a line, as described in the problem statement.