<p>You are given an array <code>nums</code> consisting of <strong>positive</strong> integers and an integer <code>k</code>.</p>

<p><strong>Partition</strong> the array into two ordered <strong>groups</strong> such that each element is in exactly <strong>one</strong> group. A partition is called great if the <strong>sum</strong> of elements of each group is greater than or equal to <code>k</code>.</p>

<p>Return <em>the number of <strong>distinct</strong> great partitions</em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>Two partitions are considered distinct if some element <code>nums[i]</code> is in different groups in the two partitions.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4], k = 4
<strong>Output:</strong> 6
<strong>Explanation:</strong> The great partitions are: ([1,2,3], [4]), ([1,3], [2,4]), ([1,4], [2,3]), ([2,3], [1,4]), ([2,4], [1,3]) and ([4], [1,2,3]).
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,3,3], k = 4
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no great partitions for this array.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [6,6], k = 2
<strong>Output:</strong> 2
<strong>Explanation:</strong> We can either put nums[0] in the first partition or in the second partition.
The great partitions will be ([6], [6]) and ([6], [6]).
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length, k &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def countPartitions(self, nums: List[int], k: int) -> int:
        MOD = 10 ** 9 + 7
  
        def helper2(a, i, target, k, dp):
            if i == len(a):
                if target < k:
                    return 1
                return 0
            if dp[i][target] != -1:
                return dp[i][target]
            
            left, right = 0, 0
            if (target + a[i] < k):
                left = helper2(a, i + 1, target + a[i], k, dp)
            right = helper2(a, i + 1, target, k, dp)
            dp[i][target] = left + right
            return dp[i][target]

        
        total = 0
        for i in nums:
            total = (total + i) % MOD
        
        if total // 2 < k:
            return 0
            
        dp = [[-1 for _ in range(k)] for _ in range(len(nums))]

        w = helper2(nums, 0, 0, k, dp)

        tot = 2 ** len(nums) % MOD
        # for i in range(len(nums)):
        #     tot = (tot * 2) % MOD
        return (tot - 2 * w )% MOD

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