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"content": "<p>You are given an array <code>nums</code> consisting of <strong>positive</strong> integers and an integer <code>k</code>.</p>\n\n<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>\n\n<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>\n\n<p>Two partitions are considered distinct if some element <code>nums[i]</code> is in different groups in the two partitions.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4], k = 4\n<strong>Output:</strong> 6\n<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]).\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,3,3], k = 4\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no great partitions for this array.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [6,6], k = 2\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We can either put nums[0] in the first partition or in the second partition.\nThe great partitions will be ([6], [6]) and ([6], [6]).\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length, k <= 1000</code></li>\n\t<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"If the sum of the array is smaller than 2*k, then it is impossible to find a great partition.",
"Solve the reverse problem, that is, find the number of partitions where the sum of elements of at least one of the two groups is smaller than k."
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