Hailstone HOTPO

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 32768/32768 K (Java/Others)

Description

The hailstone sequence is formed in the following way:

(1) If n is even, divide it by 2 to get n'
(2) 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 a single integer P, (1<= P <= 100000), which is the number of data set s 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, (1 <= n <= 100,000), 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.

Sample Input

4 1 1 2 3 3 9999 4 100000

Sample Output

1 1 2 16 3 101248 4 100000

Hint

liuyiding

Source

Greater New York 2012

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