You are given an integer array nums.
The strength of the array is defined as the bitwise OR of all its elements.
A subsequence is considered effective if removing that subsequence strictly decreases the strength of the remaining elements.
Return the number of effective subsequences in nums. Since the answer may be large, return it modulo 109 + 7.
The bitwise OR of an empty array is 0.
Example 1:
Input: nums = [1,2,3]
Output: 3
Explanation:
1 OR 2 OR 3 = 3.[1, 3]: The remaining element [2] has a Bitwise OR of 2.[2, 3]: The remaining element [1] has a Bitwise OR of 1.[1, 2, 3]: The remaining elements [] have a Bitwise OR of 0.Example 2:
Input: nums = [7,4,6]
Output: 4
Explanation:
7 OR 4 OR 6 = 7.[7]: The remaining elements [4, 6] have a Bitwise OR of 6.[7, 4]: The remaining element [6] has a Bitwise OR of 6.[7, 6]: The remaining element [4] has a Bitwise OR of 4.[7, 4, 6]: The remaining elements [] have a Bitwise OR of 0.Example 3:
Input: nums = [8,8]
Output: 1
Explanation:
8 OR 8 = 8.[8, 8] is effective since removing it leaves [] which has a Bitwise OR of 0.Example 4:
Input: nums = [2,2,1]
Output: 5
Explanation:
2 OR 2 OR 1 = 3.[1]: The remaining elements [2, 2] have a Bitwise OR of 2.[2, 1] (using nums[0], nums[2]): The remaining element [2] has a Bitwise OR of 2.[2, 1] (using nums[1], nums[2]): The remaining element [2] has a Bitwise OR of 2.[2, 2]: The remaining element [1] has a Bitwise OR of 1.[2, 2, 1]: The remaining elements [] have a Bitwise OR of 0.
Constraints:
1 <= nums.length <= 1051 <= nums[i] <= 106