# Time:  O(n)
# Space: O(1)

# Given an array of integers with possible duplicates,
# randomly output the index of a given target number.
# You can assume that the given target number must exist in the array.
#
# Note:
# The array size can be very large.
# Solution that uses too much extra space will not pass the judge.
#
# Example:
#
# int[] nums = new int[] {1,2,3,3,3};
# Solution solution = new Solution(nums);
#
# // pick(3) should return either index 2, 3, or 4 randomly.
# Each index should have equal probability of returning.
# solution.pick(3);
#
# // pick(1) should return 0. Since in the array only nums[0] is equal to 1.
# solution.pick(1);

from random import randint

class Solution(object):

    def __init__(self, nums):
        """

        :type nums: List[int]
        :type numsSize: int
        """
        self.__nums = nums

    def pick(self, target):
        """
        :type target: int
        :rtype: int
        """
        reservoir = -1
        n = 0
        for i in xrange(len(self.__nums)):
            if self.__nums[i] != target:
                continue
            reservoir = i if randint(1, n+1) == 1 else reservoir
            n += 1
        return reservoir


# Your Solution object will be instantiated and called as such:
# obj = Solution(nums)
# param_1 = obj.pick(target)