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 pi (0 < pi < 100 for 1 <= i <= k). For each i (n <= i <= k) he computes Pi(m) and Pi(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 Pi(m) > Pi(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 Pi(m) < Pi(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.

The first line of the input 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 pi is specified with two digits after decimal point. Prices in the input file are such that Pi(m) != Pi(n) for all i (n <= i <= k).

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

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