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

<https://leetcode.com/problems/number-of-subsequences-that-satisfy-the-given-sum-condition>

## Description

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 `109 + 7`.

**Example 1:**

```
**Input:** nums = [3,5,6,7], target = 9
**Output:** 4
**Explanation:** There are 4 subsequences that satisfy the condition.
[3] -> Min value + max value <= target (3 + 3 <= 9)
[3,5] -> (3 + 5 <= 9)
[3,5,6] -> (3 + 6 <= 9)
[3,6] -> (3 + 6 <= 9)
```

**Example 2:**

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

**Example 3:**

```
**Input:** nums = [2,3,3,4,6,7], target = 12
**Output:** 61
**Explanation:** There are 63 non-empty subsequences, two of them don't satisfy the condition ([6,7], [7]).
Number of valid subsequences (63 - 2 = 61).
```

**Example 4:**

```
**Input:** nums = [5,2,4,1,7,6,8], target = 16
**Output:** 127
**Explanation:** All non-empty subset satisfy the condition (2^7 - 1) = 127
```

**Constraints:**

* `1 <= nums.length <= 105`
* `1 <= nums[i] <= 106`
* `1 <= target <= 106`

## ac

```java
```


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