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Competitions

DSA Week 1

Hailstone HOTPO

The hailstone sequence is formed in the following way:

  • If n is even, divide it by 2 to get n
  • if n is odd, multiply it by 3 and add 1 to get n

It is conjectured that for any positive integer number n, the sequence will always end in the repeating cycle: 4, 2, 1, 4, 2, 1, ... Suffice to say, when n = 1, we will say the sequence has ended.

Write a program to determine the largest value in the sequence for a given n.

Input

The first line of input contains the number of data sets t (1t100000) that follow. Each data set should be processed identically and independently.

Each data set consists of a single line of input consisting of two space separated decimal integers. The first integer is the data set number. The second integer is n (ln100000), which is the starting value.

Output

For each data set there is a single line of output consisting of the data set number, a single space, and the largest value in the sequence starting at and including n.

Time limit 3 seconds
Memory limit 128 MiB
Input example #1
4
1 1
2 3
3 9999
4 100000
Output example #1
1 1
2 16
3 101248
4 100000
Source 2012 Greater New York Region Programming Contest, October 28, Problem A