Fibonacci numbers are the sequence of integers: f 0 = 0 , f 1 = 1 , f 2 = 1 , f 3 = 2 , f 4 = 3 , f 5 = 5 , ... , f n = f n - 2 + f n - 1 . So every next number is the sum of the previous two. Bajtek has developed a nice way to compute Fibonacci numbers on a blackboard. First, he writes a 0. Then, below it, he writes a 1. Then he performs the following two operations: operation " T ": replace the top number with the sum of both numbers; operation " B ": replace the bottom number with the sum of both numbers. If he performs n operations, starting with " T " and then choosing operations alternately (so that the sequence of operations looks like " TBTBTBTB ... "), the last number written will be equal to f n + 1 . Unfortunately, Bajtek sometimes makes mistakes and repeats an operation two or more times in a row. For example, if Bajtek wanted to compute f 7 , then he would want to do n = 6 operations: " TBTBTB ". If he instead performs the sequence of operations " TTTBBT ", then he will have made 3 mistakes, and he will incorrectly compute that the seventh Fibonacci number is 10. The number of mistakes in the sequence of operations is the number of neighbouring equal operations (« TT » or « BB »). You are given the number n of operations that Bajtek has made in an attempt to compute f n + 1 and the number r that is the result of his computations (that is last written number). Find the minimum possible number of mistakes that Bajtek must have made and any possible sequence of n operations resulting in r with that number of mistakes. Assume that Bajtek always correctly starts with operation " T ". The first line contains the integers n and r ( 1 ≤ n , r ≤ 10 6 ) . The first line of the output should contain one number — the minimum possible number of mistakes made by Bajtek. The second line should contain n characters, starting with " T ", describing one possible sequence of operations with that number of mistakes. Each character must be either " T " or " B ". I