<p>You are given an array of integers <code>nums</code> and an integer <code>target</code>.</p>

<p>Return <em>the number of <strong>non-empty</strong> subsequences of </em><code>nums</code><em> such that the sum of the minimum and maximum element on it is less or equal to </em><code>target</code>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [3,5,6,7], target = 9
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 4 subsequences that satisfy the condition.
[3] -&gt; Min value + max value &lt;= target (3 + 3 &lt;= 9)
[3,5] -&gt; (3 + 5 &lt;= 9)
[3,5,6] -&gt; (3 + 6 &lt;= 9)
[3,6] -&gt; (3 + 6 &lt;= 9)
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,3,6,8], target = 10
<strong>Output:</strong> 6
<strong>Explanation:</strong> There are 6 subsequences that satisfy the condition. (nums can have repeated numbers).
[3] , [3] , [3,3], [3,6] , [3,6] , [3,3,6]
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,3,3,4,6,7], target = 12
<strong>Output:</strong> 61
<strong>Explanation:</strong> There are 63 non-empty subsequences, two of them do not satisfy the condition ([6,7], [7]).
Number of valid subsequences (63 - 2 = 61).
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= target &lt;= 10<sup>6</sup></code></li>
</ul>

"""
1498. Number of Subsequences That Satisfy the Given Sum Condition

You are given an array of integers nums and an integer target.

Return the number of non-empty subsequences of nums such that the sum of the
minimum and maximum element on it is less or equal to target.
Since the answer may be too large, return it modulo 10^9 + 7.
"""
from typing import List

MOD = 1_000_000_007

class Solution:
    def numSubseq(self, nums: List[int], target: int) -> int:
        def find_index(arr: List[int], target: int, start_index) -> int:
            index = -1
            left, right = start_index, len(arr) - 1
            while left <= right:
                mid = left + (right - left) // 2
                if arr[mid] <= target:
                    index = mid
                    left = mid + 1
                else:
                    right = mid - 1

            return index

        nums.sort()
        count = 0

        for i in range(len(nums)):
            index = find_index(nums, target - nums[i], i)
            if index != -1:
                count = (count + (1 << (index - i))) % MOD

        return count

1379