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

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

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

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

<p>Tests are generated such that the answer will not exceed <code>10<sup>7</sup></code> and <code>hour</code> will have <strong>at most two digits after the decimal point</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> dist = [1,3,2], hour = 6
<strong>Output:</strong> 1
<strong>Explanation: </strong>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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> dist = [1,3,2], hour = 2.7
<strong>Output:</strong> 3
<strong>Explanation: </strong>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.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> dist = [1,3,2], hour = 1.9
<strong>Output:</strong> -1
<strong>Explanation:</strong> It is impossible because the earliest the third train can depart is at the 2 hour mark.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == dist.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= dist[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= hour &lt;= 10<sup>9</sup></code></li>
	<li>There will be at most two digits after the decimal point in <code>hour</code>.</li>
</ul>

class Solution:
    def minSpeedOnTime(self, dist: List[int], hour: float) -> int:
        n = len(dist)
        def condition(speed):
            time = 0
            
            for i in range(n - 1):
                time += ceil(dist[i] / speed)
            time += dist[n - 1] / speed
            return time <= hour
            
            
        l, r = 1, 1e7 + 1
        while l < r:
            m = (l + r) // 2
            if condition(m):
                r = m
            else:
                l = m + 1
        return int(l) if l < 1e7 + 1 else -1
2014