Staircase Numbers

Medium

Call a number a staircase if each of its digits is exactly one more than the digit before it, like 3456. You are given two integers lo and hi. Return every staircase number in the range [lo, hi], both ends included, in increasing order.

Example 1

lo=40, hi=80 → [45, 56, 67, 78]

In this range the digits climb step by step in 45, 56, 67 and 78.

Example 2

lo=780, hi=2300 → [789, 1234]

The three-digit 789 and the four-digit 1234 fit; the next one, 2345, is already above 2300.

Example 3

lo=90, hi=99 → []

No digit follows 9, and 89 is below 90, so there are no such numbers.

Constraints

10 ≤ lo ≤ hi ≤ 10⁹

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Topics

Enumeration

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Input

lo=40, hi=80

Expected

[45, 56, 67, 78]

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