Eating Speed

There are piles of bananas, piles[i] in pile i. You eat at a speed of k bananas per hour. Each hour you pick one pile and eat up to k bananas from it; if the pile has fewer than k left you finish it and waste the rest of that hour.

Return the smallest whole k that lets you finish every pile within hours hours.

Examples

Example 1

Input:

min_eating_speed([3, 6, 7, 11], 8)

Output:

4

Speed 4 takes 1 + 2 + 2 + 3 = 8 hours.

Example 2

Input:

min_eating_speed([30, 11, 23, 4, 20], 5)

Output:

30

With 5 hours for 5 piles you must finish a pile every hour, so the speed is the biggest pile: 30.

Constraints

• 1 <= len(piles) <= 2 * 10**4
• len(piles) <= hours <= 10**9
• 1 <= piles[i] <= 10**9
• Trying every speed one by one is too slow for the large tests.