You are given an integer array nums and an integer k.

A partition of the array into two groups is considered a great partition if:

• Every element in nums belongs to exactly one of the two groups.

• The sum of elements in each group is greater than or equal to k.

Return the number of distinct great partitions. Since the answer may be large, return it modulo $10^9 + 7$.

Two partitions are considered distinct if there is at least one element of nums that is assigned to different groups in the two partitions.

Constraints:

• $1 \leq$ nums.length, k $\leq 1000$

• $1 \leq$ nums[i] $\leq 10^9$

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