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 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 historical prices p_{i}
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.

1) 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.

2) 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.

Input file format

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).

Output file format

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