Goal
Given a pair of positive integers (a, b), a ≤ b, the next term in the sequence is (a*2, b-a), re-arranged if necessary so that the first element is always the smallest.
i.e. (a, b) → (min(a*2, b-a), max(a*2, b-a))
The sequence halts if a = b ever occurs.
Examples:
(3, 7) → (4, 6) → (2, 8) → (4, 6) loops because of the cycle (4, 6) → (2, 8) → (4, 6)
(3, 7) → (7-3, 3*2) = (4, 6)
(4, 6) → (6-4, 4*2) = (2, 8)
(2, 8) → (2*2, 8-2) = (4, 6)
(13, 51) → (26, 38) → (12, 52) → (24, 40) → (16, 48) → (32, 32) halts
(5, 123) → (10, 118) → (20, 108) → (40, 88) → (48, 80) → (32, 96) → (64, 64) halts
(1, 127) → (2, 126) → (4, 124) → (8, 120) → (16, 112) → (32, 96) → (64, 64) halts
(2, 3) → (1, 4) → (2, 3) loops
(6, 7) → (1, 12) → (2, 11) → (4, 9) → (5, 8) → (3, 10) → (6, 7) loops
(12345, 123456) loops after 7411 terms
(65534, 65535) loops after 16069 terms
(16777214, 16777215) loops after 1116131 terms
(9999999, 999999999) loops after 2001133 terms
For each given pair that begins a different sequence, output "halts" if the sequence halts or "loops" if it does not halt.
Input
Integer n, number of pairs
n lines containing a pair of space-separated integers
Output
n lines containing "halts" or "loops"
Constraints
0 < a ≤ b < 2^30
0 < n < 100
Example
Input
7
3 7
2 3
6 7
1 1
13 51
5 123
1 127
Output
loops
loops
loops
halts
halts
halts
halts
