Easy Trading

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

Frank keeps a database of historical daily stock prices. His strategy has two integer parameters $m$ and $n$ ($1 \le m < n \le 100$). Every day he computes two values: $P(m)$, the average stock price over the previous $m$ days, and $P(n)$, the average stock price over the previous $n$ days. $P(m) > P(n)$ signals an upward (bullish) trend, and $P(m) < P(n)$ signals a downward (bearish) trend. In practice $P(m)$ and $P(n)$ are never equal.

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

Frank has several candidate pairs of $m$ and $n$ in mind and wants to backtest them on historical prices. He takes $k$ historical prices $p_i$ ($n < k \le 10\,000$; $0 < p_i < 100$ for $1 \le i \le k$). For each day $i$ ($n \le i \le k$) he computes $P_i(m)$ and $P_i(n)$, the arithmetic averages of $p_{i-m+1} \dots p_i$ and $p_{i-n+1} \dots p_i$ respectively.

Backtesting generates signals by these rules:

• If $P_i(m) > P_i(n)$, day $i$ has a bullish trend, and a BUY ON DAY i signal is generated when $i = n$ or day $i-1$ was bearish.
• If $P_i(m) < P_i(n)$, day $i$ has a bearish trend, and a SELL ON DAY i signal is generated when $i = n$ or day $i-1$ was bullish.

Write a program that backtests a given strategy: print the signal for the first tested day (day $n$), followed by the signals for the remaining days in increasing order of day number.

The first line contains three integers $m$, $n$, and $k$. The next $k$ lines contain the stock prices for days $1$ to $k$. Each price $p_i$ has exactly two digits after the decimal point. The prices are guaranteed to satisfy $P_i(m) \ne P_i(n)$ for all $i$ ($n \le i \le k$).

Print the list of signals, one per line, as described above.