You are given two integers, m and k, and an integer array nums.
seq is called magical if:
seq has a size of m.0 <= seq[i] < nums.length2seq[0] + 2seq[1] + ... + 2seq[m - 1] has k set bits.The array product of this sequence is defined as prod(seq) = (nums[seq[0]] * nums[seq[1]] * ... * nums[seq[m - 1]]).
Return the sum of the array products for all valid magical sequences.
Since the answer may be large, return it modulo 109 + 7.
A set bit refers to a bit in the binary representation of a number that has a value of 1.
Example 1:
Input: m = 5, k = 5, nums = [1,10,100,10000,1000000]
Output: 991600007
Explanation:
All permutations of [0, 1, 2, 3, 4] are magical sequences, each with an array product of 1013.
Example 2:
Input: m = 2, k = 2, nums = [5,4,3,2,1]
Output: 170
Explanation:
The magical sequences are [0, 1], [0, 2], [0, 3], [0, 4], [1, 0], [1, 2], [1, 3], [1, 4], [2, 0], [2, 1], [2, 3], [2, 4], [3, 0], [3, 1], [3, 2], [3, 4], [4, 0], [4, 1], [4, 2], and [4, 3].
Example 3:
Input: m = 1, k = 1, nums = [28]
Output: 28
Explanation:
The only magical sequence is [0].
Constraints:
1 <= k <= m <= 301 <= nums.length <= 501 <= nums[i] <= 108