Medium · Sorting

Sort Integers by The Power Value

Given integers 1 ≤ lo ≤ hi ≤ 1000 and 1 ≤ k ≤ hi − lo + 1, where the power of x is the number of steps to reach 1 by replacing x with x / 2 when x is even and with 3x + 1 when x is odd, sort the integers in [lo, hi] by power ascending (ties by the smaller value) and return the k-th one (1-based).

Examples

Example 1

lo=12, hi=15, k=2

Output: k-th = 13

Example 2

lo=7, hi=11, k=4

Output: k-th = 7

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