1870 - Minimum Speed to Arrive on Time\.

Medium

You are given a floating-point number hour, representing the amount of time you have to reach the office. To commute to the office, you must take n trains in sequential order. You are also given an integer array dist of length n, where dist[i] describes the distance (in kilometers) of the <code>i^th</code> train ride.

Each train can only depart at an integer hour, so you may need to wait in between each train ride.

• For example, if the <code>1^st</code> train ride takes 1.5 hours, you must wait for an additional 0.5 hours before you can depart on the <code>2^nd</code> train ride at the 2 hour mark.

Return the minimum positive integer speed (in kilometers per hour) that all the trains must travel at for you to reach the office on time, or -1 if it is impossible to be on time.

Tests are generated such that the answer will not exceed <code>10⁷</code> and hour will have at most two digits after the decimal point.

Example 1:

Input: dist = 1,3,2, hour = 6

Output: 1

Explanation: At speed 1:

• The first train ride takes 1/1 = 1 hour.

• Since we are already at an integer hour, we depart immediately at the 1 hour mark. The second train takes 3/1 = 3 hours.

• Since we are already at an integer hour, we depart immediately at the 4 hour mark. The third train takes 2/1 = 2 hours.

• You will arrive at exactly the 6 hour mark.

Example 2:

Input: dist = 1,3,2, hour = 2.7

Output: 3

Explanation: At speed 3:

• The first train ride takes 1/3 = 0.33333 hours.

• Since we are not at an integer hour, we wait until the 1 hour mark to depart. The second train ride takes 3/3 = 1 hour.

• Since we are already at an integer hour, we depart immediately at the 2 hour mark. The third train takes 2/3 = 0.66667 hours.

• You will arrive at the 2.66667 hour mark.

Example 3:

Input: dist = 1,3,2, hour = 1.9

Output: -1

Explanation: It is impossible because the earliest the third train can depart is at the 2 hour mark.

Constraints:

• n == dist.length

• <code>1 <= n <= 10⁵</code>

• <code>1 <= disti<= 10⁵</code>

• <code>1 <= hour <= 10⁹</code>

• There will be at most two digits after the decimal point in hour.