You are given an integer array nums of length n and a positive integer k.
The power of an array of integers is defined as the number of subsequences with their sum equal to k.
Return the sum of power of all subsequences of nums.
Since the answer may be very large, return it modulo 109 + 7.
\n
Example 1:
\n\nInput: nums = [1,2,3], k = 3
\n\nOutput: 6
\n\nExplanation:
\n\nThere are 5 subsequences of nums with non-zero power:
[1,2,3] has 2 subsequences with sum == 3: [1,2,3] and [1,2,3].[1,2,3] has 1 subsequence with sum == 3: [1,2,3].[1,2,3] has 1 subsequence with sum == 3: [1,2,3].[1,2,3] has 1 subsequence with sum == 3: [1,2,3].[1,2,3] has 1 subsequence with sum == 3: [1,2,3].Hence the answer is 2 + 1 + 1 + 1 + 1 = 6.
Example 2:
\n\nInput: nums = [2,3,3], k = 5
\n\nOutput: 4
\n\nExplanation:
\n\nThere are 3 subsequences of nums with non-zero power:
[2,3,3] has 2 subsequences with sum == 5: [2,3,3] and [2,3,3].[2,3,3] has 1 subsequence with sum == 5: [2,3,3].[2,3,3] has 1 subsequence with sum == 5: [2,3,3].Hence the answer is 2 + 1 + 1 = 4.
Example 3:
\n\nInput: nums = [1,2,3], k = 7
\n\nOutput: 0
\n\nExplanation: There exists no subsequence with sum 7. Hence all subsequences of nums have power = 0.
\n
Constraints:
\n\n1 <= n <= 1001 <= nums[i] <= 1041 <= k <= 100j with the sum of elements k, it contributes 2n - j to the answer.",
"Let dp[i][j] represent the number of subsequences in the subarray nums[0..i] which have a sum of j.",
"We can find the dp[i][k] for all 0 <= i <= n-1 and multiply them with 2n - j to get final answer."
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