Every number can be expressed as the sum between unique powers of two. For example, the number 21 can be expressed as 1 + 4 + 16, which can also be written as 2^0 + 2^2 + 2^4.

Create a function that returns a sorted list of powers of two, which add together to make n.

Examples

sums_of_powers_of_two(21) ➞ [1, 4, 16]

sums_of_powers_of_two(8) ➞ [8]

sums_of_powers_of_two(63) ➞ [1, 2, 4, 8, 16, 32]

Notes

Tests will only include positive whole numbers.