<p>Given an integer array <code>nums</code> with possible <strong>duplicates</strong>, randomly output the index of a given <code>target</code> number. You can assume that the given target number must exist in the array.</p>

<p>Implement the <code>Solution</code> class:</p>

<ul>
	<li><code>Solution(int[] nums)</code> Initializes the object with the array <code>nums</code>.</li>
	<li><code>int pick(int target)</code> Picks a random index <code>i</code> from <code>nums</code> where <code>nums[i] == target</code>. If there are multiple valid i&#39;s, then each index should have an equal probability of returning.</li>
</ul>

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

<pre>
<strong>Input</strong>
[&quot;Solution&quot;, &quot;pick&quot;, &quot;pick&quot;, &quot;pick&quot;]
[[[1, 2, 3, 3, 3]], [3], [1], [3]]
<strong>Output</strong>
[null, 4, 0, 2]

<strong>Explanation</strong>
Solution solution = new Solution([1, 2, 3, 3, 3]);
solution.pick(3); // It should return either index 2, 3, or 4 randomly. Each index should have equal probability of returning.
solution.pick(1); // It should return 0. Since in the array only nums[0] is equal to 1.
solution.pick(3); // It should return either index 2, 3, or 4 randomly. Each index should have equal probability of returning.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>target</code> is an integer from <code>nums</code>.</li>
	<li>At most <code>10<sup>4</sup></code> calls will be made to <code>pick</code>.</li>
</ul>

class Solution(object):

    def __init__(self, nums):
        self.sorted = sorted(zip(nums, range(len(nums))))

    def pick(self, target):
        start = bisect.bisect_left(self.sorted, (target,))
        stop = bisect.bisect_left(self.sorted, (target + 1,))
        return self.sorted[random.choice(range(start, stop))][1]
23500